Question

Consider the following statements in S and R :

S : Both sin x and cos x are decreasing functions in the interval (pi/2, pi)

R : If a differentiable function decrease in an interval (a, b), then its derivative also decreases in (a, b).

Which of the following is true ?

(a) Both S and R are wrong

(b) Both S and R are correct, but R is not the correct explanation of S

(c) S is correct and R is correct explanation for S

(d) S is correct and R is wrong

Answer 1

Correct option (d) S is correct and R is wrong

Explanation :

Since, it is true that sin x and cos x is decreasing in the interval (pi/2, pi).

Now, let f(x)=sin x, x ∈ (pi, 3pi/3), f(x) decreases from 0 to -1 but f'(x) = cos x increases from -1 to 0.

Therefore, (d) is the answer.