Question: "Is f(x)=xcos⁡x concave or convex at x=π2?"

Brooks Barker

Answered question

2022-04-16

f (x) = x \cos x

concave or convex at

x = \frac{π}{2}

Raina Blackburn

Beginner2022-04-17Added 10 answers

Step 1
Given:

f (x) = x \cos x

f^{'} (x) = x (- \sin x) + \cos x

= - x \sin x + \cos x

f x) = - x (\cos x) - \sin x - \sin x

f x) = - x \cos x - 2 \sin x

Step 2

f \frac{π}{2}) = - \frac{π}{2} \cos (\frac{π}{2}) - 2 \sin (\frac{π}{2})

= 0 - 2 (1)

= - 2

Since

f (\frac{π}{2}) < 0

hence the given function is concave at

x = \frac{π}{2}

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