Mathematics: Calculus(derivatives): show your work ! find the minimum and maximum points of f(x)=x^3+x^2-5x-2.

Calculus(derivatives): show your work ! find

Ответ:

kesmith73

03.01.2022

Mathematics

$\implies f'(x)=3x^2+2x-5=(3x+5)(x-1)$

Critical points occur when f'(x)=0

, which happens for $x=-\dfrac53$ and x=1

.

Check the sign of the second derivative at each critical point to determine the function's concavity at that point. If it's concave ( f''(x)

), then a maximum occurs; if it's convex ( f''(x)0

), then a minimum occurs.

You have

f''(x)=6x+2

and so

$f''\left(-\dfrac53\right)=-8$
$f''(1)=80\implies f(x)\text{ is convex at }x=1$

This means a maximum of $f\left(-\dfrac53\right)=\dfrac{121}{27}$ and a minimum of f(1)=-5

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Ответ:

xoaprilox

30.06.2022

Mathematics

I really don’t know dude just here for free points
Explanation: step by step

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Calculus(derivatives):
show your work !
find the minimum and maximum points of f(x)=x^3+x^2-5x-2.

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