33 Prove that the function f(x) = cos x is : i. strictly decreasing on (0, π) ii. strictly increasing in (π, 2π) iii. neither increasing nor decreasing in (0, 2 π)

Question

Philoid · Accepted Answer

Given f(x) =cos x

(i) Since for each x (),sin x > 0

⇒

So f is strictly decreasing in (0,)

(ii) Since for each x (),sin x <0

⇒

So f is strictly increasing in (,2)

(iii) Clearly from (1) and (2) above, f is neither increasing nor decreasing in (0,)

33 Prove that the function f(x) = cos x is :i. strictly decreasing on (0, π)ii. strictly increasing in (π, 2π)iii. neither increasing nor decreasing in (0, 2 π)

33 Prove that the function f(x) = cos x is :
i. strictly decreasing on (0, π)

ii. strictly increasing in (π, 2π)

iii. neither increasing nor decreasing in (0, 2 π)