MAT 21A Lecture Notes - Lecture 15: Inverse Function, Product Rule, Quotient Rule

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MAT 21A Full Course Notes
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Mat 21a lecture 15 derivatives of inverse functions. The slope on the graph of the inverse function, f-1(x) is the reciprocal of the slope at the corresponding point on the original function, f(x) Example: if f(x) = x3 and its inverse function f-1(x) = x1/3, then: Slope of y = x3 at point (2, 8): f (x) = 3x2 at x = 2 f (2) = 3(2)2 = 12. Slope of y = x1/3 at corresponding point (8, 2): f (x) = 12 is the reciprocal to slope of 12. Problem: find the slope of inverse function for y = x3 at x = 22. If f(x) is any function and f-1(x) is its inverse function, then. ( 1( )) where f-1(x) represents the corresponding point on y = f(x) corresponding to a value of x on y = f-1(x). Example: if f(x) = x5 + 3, then find. You could find the inverse function, but this is not necessary.

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