What is the extreme f(x)=(x^3)/3+(15x^2)/2+50x-2 ?

The extreme f(x)=(x^3)/3+(15x^2)/2+50x-2 is Maximum(-10,-256/3),Minimum(-5, 875/6-252)

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extreme f(x)=(x^3)/3+(15x^2)/2+50x-2

extreme points

f (x) = \frac{x ^{3}}{3} + \frac{15 x ^{2}}{2} + 50 x - 2

Maximum (- 10, - \frac{256}{3}), Minimum (- 5, \frac{875}{6} - 252)

Solution steps

f^{'} (x) = x^{2} + 15 x + 50

Find intervals:

Increasing

: - \infty < x < - 10,

Decreasing

: - 10 < x < - 5,

Increasing

: - 5 < x < \infty

Plug

x = - 10

into

\frac{x ^{3}}{3} + \frac{15 x ^{2}}{2} + 50 x - 2 : - \frac{256}{3}

Maximum (- 10, - \frac{256}{3})

Plug

x = - 5

into

\frac{x ^{3}}{3} + \frac{15 x ^{2}}{2} + 50 x - 2 : \frac{875}{6} - 252

Minimum (- 5, \frac{875}{6} - 252)

Maximum (- 10, - \frac{256}{3}), Minimum (- 5, \frac{875}{6} - 252)

y = x^{\frac{6}{7}} (x^{2} - 4)

f (x) = 3 x^{3} - 3 x^{2} - 3 x + 2

f (x) = 3 x^{3} - 3 x^{2} - 3 x + 8

f (x, y) = x^{2} + (y - 1)^{2}

f (x, y) = 10 - x^{2} - y^{2}

What is the extreme f(x)=(x^3)/3+(15x^2)/2+50x-2 ?
The extreme f(x)=(x^3)/3+(15x^2)/2+50x-2 is Maximum(-10,-256/3),Minimum(-5, 875/6-252)