What is the extreme f(x)=x^3-12x^2+45x+2 ?

The extreme f(x)=x^3-12x^2+45x+2 is Maximum(3,56),Minimum(5,52)

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extreme f(x)=x^3-12x^2+45x+2

extreme points

f (x) = x^{3} - 12 x^{2} + 45 x + 2

Maximum (3, 56), Minimum (5, 52)

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 + 2 : 56

Maximum (3, 56)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 2 : 52

Minimum (5, 52)

Maximum (3, 56), Minimum (5, 52)

f (x) = - 5 x^{3} - 4 x^{4}

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

f (x) = x^{2} + 3 y^{2} - 2 x + 18 y

f (x) = - x^{2} - x + 1, - 1 \leq x \leq 1

f (x) = e^{0.5 x} + 25 6^{- 0.5 x}

What is the extreme f(x)=x^3-12x^2+45x+2 ?
The extreme f(x)=x^3-12x^2+45x+2 is Maximum(3,56),Minimum(5,52)