What is the extreme 5x^3-30x^2+45x ?

The extreme 5x^3-30x^2+45x is Maximum(1,20),Minimum(3,0)

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extreme 5x^3-30x^2+45x

extreme points

5 x^{3} - 30 x^{2} + 45 x

Maximum (1, 20), Minimum (3, 0)

Solution steps

f^{'} (x) = 15 x^{2} - 60 x + 45

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

5 x^{3} - 30 x^{2} + 45 x : 20

Maximum (1, 20)

Plug

x = 3

into

5 x^{3} - 30 x^{2} + 45 x : 0

Minimum (3, 0)

Maximum (1, 20), Minimum (3, 0)

f (x) = - x + 2 cos (x), 0 \leq x \leq 2 π

+ (x - 1)^{2}

f (x) = 2 x^{\frac{5}{3}} - 3 x^{\frac{2}{3}}

y = sin (x) cos (x), 0 \leq x \leq π

f (x, y) = 2 x^{4} - x^{2} + 10 y^{2}

What is the extreme 5x^3-30x^2+45x ?
The extreme 5x^3-30x^2+45x is Maximum(1,20),Minimum(3,0)