What is the extreme f(x)=x^3-2x^2-15x+52.2 ?

The extreme f(x)=x^3-2x^2-15x+52.2 is Maximum(-5/3 ,67.01481…),Minimum(3,16.2)

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extreme f(x)=x^3-2x^2-15x+52.2

extreme points

f (x) = x^{3} - 2 x^{2} - 15 x + 52.2

Maximum (- \frac{5}{3}, 67.01481 \dots), Minimum (3, 16.2)

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 + 52.2 : 67.01481 \dots

Maximum (- \frac{5}{3}, 67.01481 \dots)

Plug

x = 3

into

x^{3} - 2 x^{2} - 15 x + 52.2 : 16.2

Minimum (3, 16.2)

Maximum (- \frac{5}{3}, 67.01481 \dots), Minimum (3, 16.2)

f (x) = 3 x^{2} - 5 y^{2} - 255 x + 70 y + 23

f (x) = 5 x e^{- x} + 9

f (x, y) = 3 x^{2} + 2 y^{2} - 4 y + 10 y

E (a, b) = (a + b)^{2} - (a - b)^{2}

g (x) = x^{2} - 10 x + 27

What is the extreme f(x)=x^3-2x^2-15x+52.2 ?
The extreme f(x)=x^3-2x^2-15x+52.2 is Maximum(-5/3 ,67.01481…),Minimum(3,16.2)