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Differentiation Lesson 1. Chapter 7. Gradient = . We need to be able to find the gradient of a straight line joining two points:. Find the gradient of the line joining (4, -11) and (-2, 7). Describe the way the gradient is changing on these graphs:. Finding the gradient of a curve.
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DifferentiationLesson 1 Chapter 7
Gradient = We need to be able to find the gradient of a straight line joining two points: Find the gradient of the line joining (4, -11) and (-2, 7)
Finding the gradient of a curve (differentiation)
How can you find the gradient of a curve if it keeps changing??
E.g. the function y = x2 Go to GSP file
The ideal way to find a gradient of a curve is to find the gradient of the tangent at the point we are interested in
Finding the gradient • The process of finding the gradient of a curve is called “differentiation” • You can differentiate any function to find its gradient
The function The derivative (or differential) of the function In general it can be shown that If f(x) = xn where n is a real number Then f ’(x) = nxn-1 f(x) = xn
The function The derivative (or differential) of the function. This is the gradient function In general it can be shown that f(x) = xn f ’(x) = nxn-1
f(x) = xn f ’(x) = nxn-1 In other words… E.g. 1 -1 1) Multiply function by power of x 2) Subtract 1 from the power
f(x) = xn f ’(x) = nxn-1 In other words… E.g. 1 1) Multiply function by power of x 2) Subtract 1 from the power