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

The extreme f(x)=x^3-12x^2+45x+3 is Maximum(3,57),Minimum(5,53)

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

extreme points

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

Maximum (3, 57), Minimum (5, 53)

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 + 3 : 57

Maximum (3, 57)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 3 : 53

Minimum (5, 53)

Maximum (3, 57), Minimum (5, 53)

f (x, y) = 1 + 2 x^{2} + 2 y^{2}

(x^{2} - 7 x) (y^{2} - 5 y)

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

y = 2 x^{3} - 3 x^{2} + 6

f (x) = x^{2} - 2 x^{4}

What is the extreme f(x)=x^3-12x^2+45x+3 ?
The extreme f(x)=x^3-12x^2+45x+3 is Maximum(3,57),Minimum(5,53)