What is the extreme f(x)=3x^2-8x^3+6x^2+3 ?

The extreme f(x)=3x^2-8x^3+6x^2+3 is Minimum(0,3),Maximum(3/4 , 75/16)

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extreme f(x)=3x^2-8x^3+6x^2+3

extreme points

f (x) = 3 x^{2} - 8 x^{3} + 6 x^{2} + 3

Minimum (0, 3), Maximum (\frac{3}{4}, \frac{75}{16})

Solution steps

f^{'} (x) = - 24 x^{2} + 18 x

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < \frac{3}{4},

Decreasing

: \frac{3}{4} < x < \infty

Plug

x = 0

into

3 x^{2} - 8 x^{3} + 6 x^{2} + 3 : 3

Minimum (0, 3)

Plug

x = \frac{3}{4}

into

3 x^{2} - 8 x^{3} + 6 x^{2} + 3 : \frac{75}{16}

Maximum (\frac{3}{4}, \frac{75}{16})

Minimum (0, 3), Maximum (\frac{3}{4}, \frac{75}{16})

f (x) = - e^{(a (4 - x))} + 1

Z (x, y) = x + y - (\frac{x \cdot y}{100})

sin (θ) - 3 cos (θ)

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

f (x, y) = 7 (\frac{1}{5} (y + 3) e^{- x y})

What is the extreme f(x)=3x^2-8x^3+6x^2+3 ?
The extreme f(x)=3x^2-8x^3+6x^2+3 is Minimum(0,3),Maximum(3/4 , 75/16)