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

The extreme f(x)=-3x^4-2x^3+9x^2 is Maximum(-3/2 , 189/16),Minimum(0,0),Maximum(1,4)

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

extreme points

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

Maximum (- \frac{3}{2}, \frac{189}{16}), Minimum (0, 0), Maximum (1, 4)

Solution steps

f^{'} (x) = - 12 x^{3} - 6 x^{2} + 18 x

Find intervals:

Increasing

: - \infty < x < - \frac{3}{2},

Decreasing

: - \frac{3}{2} < x < 0,

Increasing

: 0 < x < 1,

Decreasing

: 1 < x < \infty

Plug

x = - \frac{3}{2}

into

- 3 x^{4} - 2 x^{3} + 9 x^{2} : \frac{189}{16}

Maximum (- \frac{3}{2}, \frac{189}{16})

Plug

x = 0

into

- 3 x^{4} - 2 x^{3} + 9 x^{2} : 0

Minimum (0, 0)

Plug

x = 1

into

- 3 x^{4} - 2 x^{3} + 9 x^{2} : 4

Maximum (1, 4)

Maximum (- \frac{3}{2}, \frac{189}{16}), Minimum (0, 0), Maximum (1, 4)

y = \frac{x}{x ^{2} + 49}

(x - 8) ln (x - 8)

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

f (x) = - 15 + 7 x - x^{2}

f (x) = \frac{0.002 x ^{2} + 24}{x}

What is the extreme f(x)=-3x^4-2x^3+9x^2 ?
The extreme f(x)=-3x^4-2x^3+9x^2 is Maximum(-3/2 , 189/16),Minimum(0,0),Maximum(1,4)