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Question
If f(x) = |cosx – sinx| , then `"f'"(pi/4)` = ______.
Solution
If f(x) = |cosx – sinx| , then `"f'"(pi/4)` = `(sqrt(3) + 1)/2`.
Explanation:
Given that: f(x) = |cosx – sinx|
We know that sin x > cos x if x ∈ `(pi/4, pi/2)`
⇒ cos x – sin x < 0
∴ f(x) = – (cos x – sin x)
f'(x) = – (– sin x – cos x)
⇒ f'(x) = (sin x + cos x)
∴ `"f'"(pi/3) = sin pi/3 + cos pi/3`
= `sqrt(3)/2 + 1/2`
= `(sqrt(3) + 1)/2`
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