Question

Consider the following statements :
1. The function f(x) = sin x decreases on the interval $(0,\pi /2)$.
2. The function f(x) = cos x increases on the interval $(0,\pi /2)$.
Which of the above statements is/are correct ?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

Answer: (D)

Neither 1 nor 2

For $f\left(x\right)=\sin x,f^{{}^{\prime }}\left(x\right)=\cos x$, which is always positive in the interval $(0,\frac{\pi }{2})$ ,

Hence the function $f\left(x\right)=\sin x$ is always increasing in the interval$(0,\frac{\pi }{2})$

For $f\left(x\right)=\cos x,f^{{}^{\prime }}\left(x\right)=-\sin x$, which is always negative in the interval $(0,\frac{\pi }{2})$ ,

Hence the function $f\left(x\right)=\cos x$ is always decreasing in the interval$(0,\frac{\pi }{2})$