For what values of x is \(\displaystyle{f{{\left({x}\right)}}}={\left({x}+{6}\right)}{\left({x}-{1}\right)}{\left({x}+{3}\right)}\)

Charlotte Holden

Charlotte Holden

Answered question

2022-04-12

For what values of x is f(x)=(x+6)(x1)(x+3) concave or convex?

Answer & Explanation

Egerlandsq0z

Egerlandsq0z

Beginner2022-04-13Added 14 answers

Step 1
A function is convex where its second derivative is positive and concave where its second derivative is negative. If its second derivative is 0, then the function may be concave, convex or neither. Commonly such will be a point of inflexion.
Given: f(x)=(x+6)(x1)(x+3)
x3+8x2+9x18
Step 2
We find: f(x)=3x2+16x+9
and f(x)=6x+16
Hence f(x) is concave for x(,83) and convex for x(83,)
It has a point of infexion at x=83

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