Consider the function $f(x) =\sin x$ in the interval $[π, 2π]$, then which of the following statements are correct?
(A) $x =\frac{3\pi}{2}$ is its stationary point.
(B) Its maximum value is 1
(C) Its minimum value is -1
(D) It attains its maximum value at $π$ and $2π$
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
$f(x)=\sin x,\; x\in[\pi,2\pi]$
$\frac{d}{dx}(\sin x)=\cos x$
$\cos x=0$ at $x=\frac{3\pi}{2}$ inside $[\pi,2\pi]$.
Hence $x=\frac{3\pi}{2}$ is a stationary point.
$\sin x$ on $[\pi,2\pi]$ decreases from $0$ (at $x=\pi$) to $-1$ (at $x=\frac{3\pi}{2}$) and then increases back to $0$ (at $x=2\pi$).
Maximum value $=0$ at $x=\pi,2\pi$.
Minimum value $=-1$ at $x=\frac{3\pi}{2}$.
The correct statements are (A), (C) and (D).