For what values of x is \(\displaystyle{f{{\left({x}\right)}}}=-{x}^{{{3}}}-{4}{x}^{{{2}}}+{2}{x}+{5}\)

Brooks Barker

Brooks Barker

Answered question

2022-04-14

For what values of x is f(x)=x34x2+2x+5 concave or convex?

Answer & Explanation

Gonarsu2dw8

Gonarsu2dw8

Beginner2022-04-15Added 19 answers

Step 1
Use the second differential to decide concavity. If f(x)>0 then the curve is convex, and if f(x)<0 then it is concave. Convex means the gradient is decreasing (going from positive to negative), and concave means the gradient is increasing (going form negative to positive).
f(x)=3x28x+2
f(x)=6x8
6x8>0x>8643
The curve is convex for x43 and concave for x<43

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