What is the extreme f(x)=4x^3+9x^2-12x+10 ?

The extreme f(x)=4x^3+9x^2-12x+10 is Maximum(-2,38),Minimum(1/2 , 27/4)

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extreme f(x)=4x^3+9x^2-12x+10

extreme points

f (x) = 4 x^{3} + 9 x^{2} - 12 x + 10

Maximum (- 2, 38), Minimum (\frac{1}{2}, \frac{27}{4})

Solution steps

f^{'} (x) = 12 x^{2} + 18 x - 12

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < \frac{1}{2},

Increasing

: \frac{1}{2} < x < \infty

Plug

x = - 2

into

4 x^{3} + 9 x^{2} - 12 x + 10 : 38

Maximum (- 2, 38)

Plug

x = \frac{1}{2}

into

4 x^{3} + 9 x^{2} - 12 x + 10 : \frac{27}{4}

Minimum (\frac{1}{2}, \frac{27}{4})

Maximum (- 2, 38), Minimum (\frac{1}{2}, \frac{27}{4})

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

- 2 x^{2} - 900

y, f = - \frac{40000 x}{( 3 + x ^{2} + 2 y ^{2} ) ^{2}}

f (x) = (x^{3} - 3 x) (y + 3) + y (y + 6)

4 h^{3} - 96 h^{2} + 527 h

What is the extreme f(x)=4x^3+9x^2-12x+10 ?
The extreme f(x)=4x^3+9x^2-12x+10 is Maximum(-2,38),Minimum(1/2 , 27/4)