Find the absolute maximum value for the function $f ( x ) = 2 \sin x \cos x \text { for } 0 \leq x \leq \pi$
A) $1$

B) - 2
C) $\frac { 1 } { 4 }$
D)0
E) - 1
F)2
G) $\frac { 1 } { 2 }$

H)No absolute minimum

Question

Find the absolute maximum value for the function $f ( x ) = 2 \sin x \cos x \text { for } 0 \leq x \leq \pi$
A) $1$

B) - 2
C) $\frac { 1 } { 4 }$ 
D)0
E) - 1
F)2
G) $\frac { 1 } { 2 }$

H)No absolute minimum

Quizplus · Accepted Answer

The function $f(x) = 2\sin x \cos x$ can be rewritten as $f(x) = \sin(2x)$ using the double angle formula. The sine function has a maximum value of 1 within its range, and since $2x$ ranges from $0$ to $2\pi$ within the given domain $0 \leq x \leq \pi$, the maximum value of $f(x)$ is indeed 1.

Find the Absolute Maximum Value for the Function f(x)=2sin⁡xcos⁡x for 0≤x≤πf ( x ) = 2 \sin x \cos x \text { for } 0 \leq x \leq \pif(x)=2sinxcosx for 0≤x≤π

Find the Absolute Maximum Value for the Function $f ( x ) = 2 \sin x \cos x \text { for } 0 \leq x \leq \pi$