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Question: f(x) = \(\left\{ \begin{array} { l l } \tan ^ { - 1 } x , & | x | \leq \frac { \pi } { 4 } \\ \frac ...

f(x) = {tan⁡−1x,∣x∣≤π4π2−∣x∣,∣x∣≥π4\left\{ \begin{array} { l l } \tan ^ { - 1 } x , & | x | \leq \frac { \pi } { 4 } \\ \frac { \pi } { 2 } - | x | , & | x | \geq \frac { \pi } { 4 } \end{array} \right.then

A

f(x) has no point of local maxima

B

f(x) has no point of local minima

C

f(x) has exactly two points of local maxima

D

f(x) has exactly two points of local minima

Answer

f(x) has exactly two points of local maxima

Explanation

Solution

Clearly tan⁡−1(π4)<π4\tan ^ { - 1 } \left( \frac { \pi } { 4 } \right) < \frac { \pi } { 4 }. Thus x = ±π4\pm \frac { \pi } { 4 } are the points of local maxima for f(x).