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Popular Functions >

extreme 6x^2-3x^3

Solution

extreme

Solution

Minimum (0, 0), Maximum (\frac{4}{3}, \frac{32}{9})

Solution steps

f^{'} (x) = 12 x - 9 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

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

Decreasing

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

Plug

x = 0

into

6 x^{2} - 3 x^{3} : 0

Minimum (0, 0)

Plug

x = \frac{4}{3}

into

6 x^{2} - 3 x^{3} : \frac{32}{9}

Maximum (\frac{4}{3}, \frac{32}{9})

Minimum (0, 0), Maximum (\frac{4}{3}, \frac{32}{9})

Graph

Popular Examples

extreme f(x)=6x^2-12x

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extreme f(x)=-x^3+15x^2+13

extreme x^{1/3}(x^2-9),-4<= x<= 2

extreme f(x)=xe^{-x^2}[0.2]

Frequently Asked Questions (FAQ)

What is the extreme 6x^2-3x^3 ?
The extreme 6x^2-3x^3 is Minimum(0,0),Maximum(4/3 , 32/9)