What is the extreme g(x)=x^3-12x^2+45x+7 ?

The extreme g(x)=x^3-12x^2+45x+7 is Maximum(3,61),Minimum(5,57)

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extreme g(x)=x^3-12x^2+45x+7

extreme points

g (x) = x^{3} - 12 x^{2} + 45 x + 7

Maximum (3, 61), Minimum (5, 57)

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 + 7 : 61

Maximum (3, 61)

Plug

x = 5

into

x^{3} - 12 x^{2} + 45 x + 7 : 57

Minimum (5, 57)

Maximum (3, 61), Minimum (5, 57)

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

f (x) = \frac{( x ^{2} - 1 )}{x ^{2} + 2 x - 3}

f (x) = - 3 t^{2} + 72 t + 243

y = - 2 x^{2} e^{- 2 x} - 2

f (x) = x (22 - 37 + 2 x) (\frac{37}{2} - x)

What is the extreme g(x)=x^3-12x^2+45x+7 ?
The extreme g(x)=x^3-12x^2+45x+7 is Maximum(3,61),Minimum(5,57)