Find the Extrema of the Function on the Given Interval $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

Multiple Choice

Find the extrema of the function on the given interval, and say where they occur.
- $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

A) local maxima: 1 at $x = \frac { \pi } { 8 }$ and 0 at $x = \frac { \pi } { 2 }$ ;
local minima: 0 at $x = 0$ and $- 1$ at $x = \frac { 3 \pi } { 8 }$

B) local maxima: 1 at $x = \frac { \pi } { 8 }$ and 0 at $x = \frac { \pi } { 2 }$ ;
local minimum: $- 1$ at $x = \frac { 3 \pi } { 8 }$

C) local maxima: 1 at $x = \frac { \pi } { 4 }$ and 0 at $x = \frac { \pi } { 2 }$ ;
local minima: 0 at $x = 0$ and $- 1$ at $x = \frac { 3 \pi } { 8 }$

D) local maxima: 1 at $x = \frac { \pi } { 8 }$ and 0 at $x = \frac { \pi } { 4 }$ ;

local minimum: 0 at $x = 0$