What is the extreme f(x)=4x^3-45x^2+150x ?

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

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extreme f(x)=4x^3-45x^2+150x

extreme points

f (x) = 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)

f (x) = ∣ 2 x + 5 ∣ - 1

f (x) = y^{6} + 5 y^{4} - 6 y^{2}

5 cos (\frac{x}{6})

f (x) = \frac{x}{4} + 2

f (x) = - 7 x + 28

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