Question

If f(x) = |cosx|, then `"f'"(pi/4)` = ______.

Answer 1

If f(x) = |cosx|, then `"f'"(pi/4)` = `- 1/sqrt(2)`.

Explanation:

Given that: f(x) = |cos x|

⇒ f(x) = cos x if x ∈ `(0, pi/2)`

Differentiating both sides w.r.t. x, we get f'(x) = – sin x

At x = `pi/4`,

`"f'"(pi/4) = - sin  pi/4`

= `- 1/sqrt(2)`.