What is the extreme x^3-12x^2+45x+6 ?

The extreme x^3-12x^2+45x+6 is Maximum(3,60),Minimum(5,56)

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extreme x^3-12x^2+45x+6

extreme points

x^{3} - 12 x^{2} + 45 x + 6

Maximum (3, 60), Minimum (5, 56)

Solution steps

f^{'} (x) = 3 x^{2} - 24 x + 45

Find intervals:

Increasing

: - \infty < x < 3,

Decreasing

: 3 < x < 5,

Increasing

: 5 < x < \infty

Plug

x = 3

into

x^{3} - 12 x^{2} + 45 x + 6 : 60

Maximum (3, 60)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 6 : 56

Minimum (5, 56)

Maximum (3, 60), Minimum (5, 56)

h (x) = 4 - 3 x^{2}, (- 2, 1)

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

\frac{3 + x}{9 - x}, - 9 \leq x \leq 0

(x - 1)^{2} (2 x - 8)

y = 4 x^{\frac{3}{4}} - x (256)

What is the extreme x^3-12x^2+45x+6 ?
The extreme x^3-12x^2+45x+6 is Maximum(3,60),Minimum(5,56)