Is \(\displaystyle{f{{\left({x}\right)}}}={\sin{{x}}}\) concave or convex at

Delilah Novak

Delilah Novak

Answered question

2022-04-14

Is f(x)=sinx concave or convex at x=1?

Answer & Explanation

bondsk384r

bondsk384r

Beginner2022-04-15Added 12 answers

Step 1
We have to know that ddxsinx=cosx and ddxcosx=sinx.
Also recall that concavity and convexity are determined through the sign of the second derivative of a function.
First finding the second derivative:
f(x)=sinx
f(x)=cosx
fx)=sinx
Step 2
If f1)>0, then f is convex (commonly called "concave up") at x=1.
If f1)<0, then f is concave (commonly called "concave down") at x=1.
We see that f1)=sin(1)08415
Since f1)>0, we see that sinx is convex ("concave up") at x=1.

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