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