Name___________________________________ Warm-up Review of Inverse Functions A one-to-one function (passes the horizontal and vertical line test) has an inverse function, which or the original function. The graph of a function’s inverse function can be found by “undoes” “reverses” reflecting over the line y = x. Example: Use the following table of select values of function to answer the questions below. f -2 0 1 3 7 x 0 3 12 5 -2 f(x) Find: Intro to Derivatives of Inverses For each problem on this page, find the equation of the tangent line at the given point. Then find the inverse and the equation of the tangent line to the inverse at the given point. 1. at = 2 tangent line: x at = 4 tangent line: x 2. at = tangent line: x –4
Name___________________________________ Warm-up Review of Inverse Functions A one-to-one function (passes the horizontal and vertical line test) has an inverse function, which “undoes” or “reverses” the original function. The graph of a function’s inverse function can be found by reflecting over the line y = x. Example: Use the following table of select values of function f to answer the questions below. x -2 0 1 3 7 f(x) 0 3 12 5 -2 Find: Intro to Derivatives of Inverses For each problem on this page, find the equation of the tangent line at the given point. Then find the inverse and the equation of the tangent line to the inverse at the given point. 1. at x = 2 tangent line: at x = 4 tangent line: 2. at x = –4 tangent line:
171206-inverse-deriv-exploration.docx