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ET 2.5: Pg 104: #7

ET 2.5: Pg 104: #7. Find the slope of the tangent line to the graph of g(x) at (2, -5). Derivative: Slope of the line tangent to the graph at a point. Also, write everything you know about a derivative. 1 st derivative is velocity. 2 nd derivative is acceleration. “P SST ” I know!.

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ET 2.5: Pg 104: #7

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  1. ET 2.5: Pg 104: #7 Find the slope of the tangent line to the graph of g(x) at (2, -5). Derivative: Slope of the line tangent to the graph at a point. Also, write everything you know about a derivative.

  2. 1st derivative is velocity 2nd derivative is acceleration “PSST” I know! Turns Volume into Surface Area Derivative can only happen when the function is continuous with the exception of a cusp. Differentiable at point c  Continuous at point c The Constant Multiple Rule Product & Quotient Rule Power rule One degree less than original function. Derivative at a max or min is zero. Chain Rule: “Stuff” Derivative: Slope of the line tangent to the graph at a point. Instantaneous rate of change. OR

  3. Ex: The derivative of 4x3 + sinx, with respect to x, is 12x2 + cosx. “With respect to x” The fact that I say you are finding the derivative with respect to x doesn’t make the problem any harder or any different. In fact, I wouldn’t need to tell you which variable you were “respecting” so to speak, because x was the only variable in the problem. BUT, Now the problems are going to have x and y in them. We will want to take the “derivative of y with respect to x”. What you are deriving. What you are respecting.

  4. Explicit Function Implicit Function y

  5. Determine the slope of the graph of at the point (3,1). Now could you write the eq. of the tangent?

  6. Assignments 2.5 • Day 1: 1, 5, 11, 13, 23, 25, 31, 41, 70 • Day 2: 43, 49, 51, 53, 57, 61, 65, 74

  7. ET 2.5b What is the purpose of implicit differentiation? Allows you to find the slope of a tangent line when the equation in the question cannot be solved for y. Copy Definition A normal line is perpendicular to a function’s tangent line at the point of tangency.

  8. We will want to take the “derivative of y with respect to x”. What you are deriving. What you are respecting.

  9. #66a Differentiate with respect to x.

  10. #66a Differentiate with respect to t. x & y are functions of t.

  11. Find dy/dx implicitly for the equation siny = x. Then find the largest interval of the form –a < y < a on which y is a differentiable function of x. x2

  12. Assignments 2.5 • Day 1: 1, 5, 11, 13, 23, 25, 31, 41a, 70 (41b fudge) • Day 2: 43, 49, 51, 53, 57, 61, 65, 74

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