What is the extreme f(x)=(2x^3)/3+3x^2-20x,(-7,5) ?

The extreme f(x)=(2x^3)/3+3x^2-20x,(-7,5) is Maximum(-5, 275/3),Minimum(2,-68/3)

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extreme f(x)=(2x^3)/3+3x^2-20x,(-7,5)

extreme points

f (x) = \frac{2 x ^{3}}{3} + 3 x^{2} - 20 x, (- 7, 5)

Maximum (- 5, \frac{275}{3}), Minimum (2, - \frac{68}{3})

Solution steps

Find the critical points:

x = - 5, x = 2

Domain of

\frac{2 x ^{3}}{3} + 3 x^{2} - 20 x, (- 7, 5) : - 7 < x < 5

Find intervals:

Increasing

: - 7 < x < - 5,

Decreasing

: - 5 < x < 2,

Increasing

: 2 < x < 5

Plug the extreme point

x = - 5

into

\frac{2 x ^{3}}{3} + 3 x^{2} - 20 x \Rightarrow y = \frac{275}{3}

Maximum (- 5, \frac{275}{3})

Plug the extreme point

x = 2

into

\frac{2 x ^{3}}{3} + 3 x^{2} - 20 x \Rightarrow y = - \frac{68}{3}

Minimum (2, - \frac{68}{3})

Maximum (- 5, \frac{275}{3}), Minimum (2, - \frac{68}{3})

What is the extreme f(x)=(2x^3)/3+3x^2-20x,(-7,5) ?
The extreme f(x)=(2x^3)/3+3x^2-20x,(-7,5) is Maximum(-5, 275/3),Minimum(2,-68/3)