What is the extreme 4x^3-45x^2+150x ?

The extreme 4x^3-45x^2+150x is Maximum(5/2 , 625/4),Minimum(5,125)

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extreme 4x^3-45x^2+150x

extreme points

4 x^{3} - 45 x^{2} + 150 x

Maximum (\frac{5}{2}, \frac{625}{4}), Minimum (5, 125)

Solution steps

f^{'} (x) = 12 x^{2} - 90 x + 150

Find intervals:

Increasing

: - \infty < x < \frac{5}{2},

Decreasing

: \frac{5}{2} < x < 5,

Increasing

: 5 < x < \infty

Plug

x = \frac{5}{2}

into

4 x^{3} - 45 x^{2} + 150 x : \frac{625}{4}

Maximum (\frac{5}{2}, \frac{625}{4})

Plug

x = 5

into

4 x^{3} - 45 x^{2} + 150 x : 125

Minimum (5, 125)

Maximum (\frac{5}{2}, \frac{625}{4}), Minimum (5, 125)

What is the extreme 4x^3-45x^2+150x ?
The extreme 4x^3-45x^2+150x is Maximum(5/2 , 625/4),Minimum(5,125)