A Summary of Curve Sketching

Dec 20, 2023

70 likes | 86 Views

This summary covers Section 3.6 of AP Calculus, focusing on curve sketching. Learn how to find the 1st and 2nd derivative, intercepts, asymptotes, critical numbers, and inflection points. Determine symmetry and analyze various aspects of the curve.

Share Presentation

Embed Code

herma

Download Presentation

A Summary of Curve Sketching

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

A Summary of Curve Sketching Section 3.6 AP Calc
Analyze: Find the 1st and 2nd Derivative Find the intercepts, asymptotes, critical numbers, inflections points, determine symmetry
Analyze:
Analyze:
Analyze:
Analyze:
Analyze:

Curve Sketching

Curve Sketching. Lesson 5.4. Motivation. Graphing calculators decrease the importance of curve sketching So why a lesson on curve sketching? A calculator graph may be misleading What happens outside specified window?

411 views • 8 slides

Cubic curve sketching

y. y. x. x. Cubic curve sketching. General form. General shape:. a < 0. a > 0. Characteristics: usually 2 humps, may or may not be asymmetrical Important point to note: If there are 3 factors, then there will be 3 x-intercepts

770 views • 10 slides

A Summary of Curve Sketching

A Summary of Curve Sketching. Lesson 4.6. How It Was Done BC (Before Calculators). How can knowledge of a function and it's derivative help graph the function? How much can you tell about the graph of a function without using your calculator's graphing?.

378 views • 9 slides

CHAPTER 3 SECTION 3.6 CURVE SKETCHING

CHAPTER 3 SECTION 3.6 CURVE SKETCHING. Graph the following functions on your calculator and make a sketch. What do you notice about the graph of a function where there is a factor that appears twice?. 1) y=(x+1)(x-2) 2 2) y= x(x+3) 2 3) y=(x+1)(x-3) 2.

1.4k views • 96 slides

Curve Sketching

Curve Sketching. C1 Section 4.6 – 4.7. y = 9 - x 2. y = 2(9 - x 2 ). f( x ). 2f( x ). (2 , 5). (2 , 10). Each point twice as far along y. Stretches in the y-axis. If we have the function y = f( x ) then: y = a f( x ) is a stretch by a factor a in the y-axis:. f( x ). f(2 x ).

294 views • 14 slides

Summary of Curve Sketching

Summary of Curve Sketching. Section 4.5. Asymptotes. Vertical – Denominator = zero Be careful to look for holes Slant – Numerator power is 1 greater than denominator power Example: To find the slant asymptote, divide the numerator by the denominator and ignore the remainder.

251 views • 3 slides

Section 3.6 – Curve Sketching

Section 3.6 – Curve Sketching. Guidelines for sketching a Curve.

236 views • 12 slides

3.6 Curve sketching

3.6 Curve sketching. Steps. Determine intercepts, asymptotes Find critical values and points of inflection Determine intervals of increase and decrease Determine relative extrema. Analyze and sketch. Analyze and sketch . Answer I. Determine intercepts. Answer II. Determine asymptotes.

252 views • 10 slides

Cubic Curve Sketching

Cubic Curve Sketching. Basic cubic shapes . Unlike quadratics cubic usually have two bumps e.g. But sometimes the have no bumps. y =x 3 -3x 2 +3. y =-x 3 +3x 2 +3. y =x 3. Example: Sketch y=(x-1)(x+2)(x+3). Here are the steps for sketching cubic curves

278 views • 7 slides

End Behavior & Curve Sketching

End Behavior & Curve Sketching. Today you will determine the graph and the end behavior of a function using the sign studies of the function, the derivative, and the second derivative. . Sign Studies Recap. Testing points for Sign Studies.

276 views • 13 slides

4.3 Using Derivatives for Curve Sketching

4.3 Using Derivatives for Curve Sketching. Example. Use the first derivative test to find the local and absolute extreme values of:.

615 views • 22 slides

Curve Sketching

Curve Sketching. section 3-A continued . A nalyzing the graph of a function Domain and Range: All real numbers except ___ Extrema and the intervals where increasing and decreasing (first derivative test) Intercepts : where the graph crosses the x-axis and the y-axis

233 views • 7 slides

Curve Sketching

Curve Sketching. The Second Derivative and Points of Inflection. Graphs that are Concave Up on the interval a < x < b where f”(x) < 0. This means that the graph lies above the tangent line at each point on the interval. Graphs that are Concave Down on the interval a < x < b where f”(x) < 0.

471 views • 6 slides

3.6 A Summary of Curve Sketching

3.6 A Summary of Curve Sketching. Pay attention or you won’t know which way to turn!. none. y-int. ( , ). x-int. ( , ). Domain:. Asymptote(s). V.A. @ x = 0. H.A. = 2. inc. inc. 0. C.N. 0. 1 st der. test. no extrema. C.N. 0. up. 0. down. Inf. pt. none.

373 views • 11 slides

1. Summary of curve sketching

1. Summary of curve sketching. Such that f’(x)=0 or f”(x) does not exist. (ii) x-intercept: if possible solve f(x)=0. ( i ) Horizontal Asymptotes. ( i ) Symmetry. If f(-x)=f(x), then f(x) is symmetric w.r.t . the y- axis. If f(-x)=-f(x), then f(x) is symmetric w.r.t . the origin.

718 views • 57 slides

Curve Sketching

Curve Sketching. TJ Krumins Rebecca Stoddard. Curve Sketching Breakdown. Find intercepts and asymptotes Take derivative Set up sign line Find critical points Take 2 nd derivative Set up sign line Find critical points Graph. The problem (dun…nun…nuh!). Y=x^3-3x^2+4 1) Find y’

546 views • 32 slides

Curve Sketching

Curve Sketching. By Dr. Julia Arnold and Mr. Richard Gill using Tan’s 5th edition Applied Calculus for the managerial , life, and social sciences text. A rational function is a function that can be expressed in the form. where both f(x) and g(x) are polynomial functions.

498 views • 35 slides

4.5 Summary of Curve Sketching *get out orange chart!

4.5 Summary of Curve Sketching *get out orange chart!. *Graph Analysis: A) Domain B) Intercepts C) Symmetry D) Asymptotes E) Inc/Dec Intervals F) Local Min’s & Max’s G) CU & CD Intervals & Pts of Inflection H) Sketch the Curve. HW – 4.5 pg. 321 # 23 & 31.

160 views • 3 slides

Chapter 4 Curve Sketching

Chapter 4 Curve Sketching. Using Derivatives instead of Plotting Points. Lets relate a graph to its derivative. Find the first derivative. Put zeroes on a number line Find the second derivative. Put zeroes on a number line Lets look at the graph here:. Slope. y′ = slope, correct?

151 views • 6 slides

Curve sketching

Curve sketching. This PowerPoint presentation shows the different stages involved in sketching the graph. Sketching the graph. Step 1: Find where the graph cuts the axes. When x = 0, y = 2, so the graph goes through the point (0, 2).

167 views • 14 slides

Using Derivatives for Curve Sketching

Greg Kelly, Hanford High School, Richland, Washington Adapted by: Jon Bannon Siena College. Photo by Vickie Kelly, 1995. Using Derivatives for Curve Sketching. Old Faithful Geyser, Yellowstone National Park. Photo by Vickie Kelly, 2007. Using Derivatives for Curve Sketching.

126 views • 11 slides

Curve Sketching

Curve Sketching. A Summary. What Steps Do I Take to Analyze the Graph of a Function The equation of a function is given. begin by looking at any restrictions to the domain of the function. Where is the function undefined? This can occur in two places:

116 views • 7 slides

More Related

A Summary of Curve Sketching

A Summary of Curve Sketching

Presentation Transcript

Curve Sketching

Cubic curve sketching

A Summary of Curve Sketching

CHAPTER 3 SECTION 3.6 CURVE SKETCHING

Curve Sketching

Summary of Curve Sketching

Section 3.6 – Curve Sketching

3.6 Curve sketching

Cubic Curve Sketching

End Behavior &amp; Curve Sketching

4.3 Using Derivatives for Curve Sketching

Curve Sketching

Curve Sketching

3.6 A Summary of Curve Sketching

1. Summary of curve sketching

Curve Sketching

Curve Sketching

4.5 Summary of Curve Sketching *get out orange chart!

Chapter 4 Curve Sketching

Curve sketching

Using Derivatives for Curve Sketching

Curve Sketching

End Behavior & Curve Sketching