What is the extreme f(x)=80x^2-52/3 x^3+x^4 ?

The extreme f(x)=80x^2-52/3 x^3+x^4 is Minimum(0,0),Maximum(5, 1375/3),Minimum(8, 1024/3)

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extreme f(x)=80x^2-52/3 x^3+x^4

extreme

Minimum (0, 0), Maximum (5, \frac{1375}{3}), Minimum (8, \frac{1024}{3})

Solution steps

f^{'} (x) = 160 x - 52 x^{2} + 4 x^{3}

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 5,

Decreasing

: 5 < x < 8,

Increasing

: 8 < x < \infty

Plug

x = 0

into

80 x^{2} - \frac{52}{3} x^{3} + x^{4} : 0

Minimum (0, 0)

Plug

x = 5

into

80 x^{2} - \frac{52}{3} x^{3} + x^{4} : \frac{1375}{3}

Maximum (5, \frac{1375}{3})

Plug

x = 8

into

80 x^{2} - \frac{52}{3} x^{3} + x^{4} : \frac{1024}{3}

Minimum (8, \frac{1024}{3})

Minimum (0, 0), Maximum (5, \frac{1375}{3}), Minimum (8, \frac{1024}{3})

What is the extreme f(x)=80x^2-52/3 x^3+x^4 ?
The extreme f(x)=80x^2-52/3 x^3+x^4 is Minimum(0,0),Maximum(5, 1375/3),Minimum(8, 1024/3)