If x tends to π, then the given function f(x) = xsinx + cosx + cos^2x is

Question

If x tends 0 to π, then the given function f(x) = xsinx + cosx + cos²x is

(A) Increasing

(B) Decreasing

(C) Neither increasing nor decreasing

(D) None of these

Answer 1

Answer is (B) Decreasing

We have

f(x) = xsinx + cosx + cos²x

Therefore,

f'(x) = sinx + xcosx - sinx - 2cosxsinx = cosx(x - 2sinx)

Hence, x → 0 to π, then f'(x) < 0. That is, f(x) is decreasing function.

Comments

answer is wrong

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As x → π then sinx →0.
Thus, x > 2 sinx
⇒ (x-2sinx) > 0
But cosx < 0
∴ f'(x) < 0
∴ f(x) is decreasing function while x → π.