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Chapter 3 | Derivatives
3.7 EXERCISES For the following exercises, use the graph of y = f ( x ) to a. sketch the graph of y = f −1 ( x ), and b. use part a. to estimate ⎛ ⎝ f −1 ⎞ ⎠ ′(1).
263.
260.
For the following exercises, use the functions y = f ( x ) to find
df dx
at x = a and
a.
b. x = f −1 ( y ).
261.
df −1 dy
at y = f ( a ).
c. Then use part b. to find
264. f ( x ) =6 x −1, x =−2 265. f ( x ) =2 x 3 −3, x =1 266. f ( x ) =9− x 2 , 0≤ x ≤3, x =2 267. f ( x ) = sin x , x =0 For each of the following functions, find ⎛ ⎝ f −1 ⎞
⎠ ′( a ).
262.
268. f ( x ) = x 2 +3 x +2, x ≥ - 3 2 , 269. f ( x ) = x 3 +2 x +3, a =0 270. f ( x ) = x + x , a =2
a =2
271. f ( x ) = x − 2 x , x <0, a =1 272. f ( x ) = x +sin x , a =0 273. f ( x ) = tan x +3 x 2 , a =0 For each of the given functions y = f ( x ), a. find the slope of the tangent line to its inverse function f −1 at the indicated point P , and
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