Expert Answer to "Is f(x)=sin⁡x concave or convex at x=π2?"

High School
Calculus and Analysis
Calculus 1
Analyzing functions

Ean Hughes

Answered question

2022-04-13

f (x) = \sin x

concave or convex at

x = \frac{π}{2}

Answer & Explanation

strasnihwhge

Beginner2022-04-14Added 14 answers

Step 1
To even find concavity, you should know what it means by concave up and concave down.
if a functions f"(x) for a point, like (0.25, 2.25) is positive, like this graph of

x^{3}

, but in its 2nd derivative form of 9x
then its concave-Up
Step 2
If a functions f"(x) for a point, like

(0.2, - 0.54)

is negative, like the graph of

3 x^{3} + 2 x + 4

, which will turn into -27x
then its concave-Down
but all of these points and graphs are linear, your looking for an point on an non-linear graph (sin(x)).
the second derivative of

\sin (x) is - \sin (x)

x = \frac{π}{2}

, the point is negative, also known as concave-down. since the graph is going negative at the interval

[0, π]

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