What is the extreme f(x)=x^3-2x^2-15x+10[-2] ?

The extreme f(x)=x^3-2x^2-15x+10[-2] is Maximum(-5/3 ,-140/27),Minimum(3,-56)

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extreme f(x)=x^3-2x^2-15x+10[-2]

extreme points

f (x) = x^{3} - 2 x^{2} - 15 x + 10 [- 2]

Maximum (- \frac{5}{3}, - \frac{140}{27}), Minimum (3, - 56)

Solution steps

f^{'} (x) = 3 x^{2} - 4 x - 15

Find intervals:

Increasing

: - \infty < x < - \frac{5}{3},

Decreasing

: - \frac{5}{3} < x < 3,

Increasing

: 3 < x < \infty

Plug

x = - \frac{5}{3}

into

x^{3} - 2 x^{2} - 15 x + 10 [- 2] : - \frac{140}{27}

Maximum (- \frac{5}{3}, - \frac{140}{27})

Plug

x = 3

into

x^{3} - 2 x^{2} - 15 x + 10 [- 2] : - 56

Minimum (3, - 56)

Maximum (- \frac{5}{3}, - \frac{140}{27}), Minimum (3, - 56)

f (x, y) = x^{2} - y^{2} + x y - 5 x

y = \frac{1}{2} x^{2} + (\frac{14 - 3 x}{4})^{2}

93000 x - 36000

f (x) = x^{4} - 32 x^{2} - 10

f (x, y) = x - 5 y

What is the extreme f(x)=x^3-2x^2-15x+10[-2] ?
The extreme f(x)=x^3-2x^2-15x+10[-2] is Maximum(-5/3 ,-140/27),Minimum(3,-56)