"Is f(x)=sin⁡x concave or convex at x=3π2?" was answered by students like you

Ashleigh Mitchell

Answered question

2022-04-15

f (x) = \sin x

concave or convex at

x = \frac{3 π}{2}

unduncjineei5r3

Beginner2022-04-16Added 19 answers

Step 1
To test if a function is concave/convex at f(a), require to find the value of f''(a)
- If

f^{″} (a) > 0

then f(x) is convex at

x = a

- If

f^{″} (a) < 0

then f(x) is concave at

x = a

Hence

f (x) = \sin x

f^{'} (x) = \cos x

and

f^{″} (x) = - \sin x

Step 2

\Rightarrow f \frac{3 π}{2}) = - \sin (\frac{3 π}{2}) = 1

Since

f \frac{3 π}{2}) > 0

then f(x) is convex at

x = \frac{3 π}{2}

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