What is the extreme f(x)=(x^3)/3-10x^2+75x+20 ?

The extreme f(x)=(x^3)/3-10x^2+75x+20 is Maximum(5, 560/3),Minimum(15,20)

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extreme f(x)=(x^3)/3-10x^2+75x+20

extreme

Maximum (5, \frac{560}{3}), Minimum (15, 20)

Solution steps

f^{'} (x) = x^{2} - 20 x + 75

Find intervals:

Increasing

: - \infty < x < 5,

Decreasing

: 5 < x < 15,

Increasing

: 15 < x < \infty

Plug

x = 5

into

\frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20 : \frac{560}{3}

Maximum (5, \frac{560}{3})

Plug

x = 15

into

\frac{x ^{3}}{3} - 10 x^{2} + 75 x + 20 : 20

Minimum (15, 20)

Maximum (5, \frac{560}{3}), Minimum (15, 20)

What is the extreme f(x)=(x^3)/3-10x^2+75x+20 ?
The extreme f(x)=(x^3)/3-10x^2+75x+20 is Maximum(5, 560/3),Minimum(15,20)