Is \(\displaystyle{f{{\left({x}\right)}}}={x}^{{{4}}}-{2}{x}^{{{3}}}-{9}{x}-{14}\) concave or convex at

Miguel Hanson

Miguel Hanson

Answered question

2022-04-15

Is f(x)=x42x39x14 concave or convex at x=1?

Answer & Explanation

StettyNagEragpouj

StettyNagEragpouj

Beginner2022-04-16Added 7 answers

Step 1
Given: f(x)=x4-2x3-9x-14
Find the derivative
f(x)=4x36x29
Step 2
Differentiate again with respect to x
f2(x)=12x212x
Step 3
Substitute x=1 in f2(x) and check for sign
f2(1)=12(1)212(1)
f2(1)=12+12
f2(1)=24
If f2(x)>0 then the curve is convex.
If f2(x)<0, then the curve is concave
We can see at x=1 the second derivative is greater than zero, hence, the curve is convex.
For further information, you can refer
Note: Concave up is same as convex and concave down is concave

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