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

The extreme f(x)=(x-2)^2(x+3^3) is Maximum(-52/3 , 97556/27),Minimum(2,0)

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

extreme points

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

Maximum (- \frac{52}{3}, \frac{97556}{27}), Minimum (2, 0)

Solution steps

f^{'} (x) = (x - 2) (3 x + 52)

Find intervals:

Increasing

: - \infty < x < - \frac{52}{3},

Decreasing

: - \frac{52}{3} < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - \frac{52}{3}

into

(x - 2)^{2} (x + 3^{3}) : \frac{97556}{27}

Maximum (- \frac{52}{3}, \frac{97556}{27})

Plug

x = 2

into

(x - 2)^{2} (x + 3^{3}) : 0

Minimum (2, 0)

Maximum (- \frac{52}{3}, \frac{97556}{27}), Minimum (2, 0)

f (x) = 2 - 12 x

x^{3} - 27 x + 5

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

f (x, y) = x^{2} + x y + y^{2} + 4 x - 7 y + 6

f (x) = - 3 x^{2} - 5, - 4 \leq x \leq 3

What is the extreme f(x)=(x-2)^2(x+3^3) ?
The extreme f(x)=(x-2)^2(x+3^3) is Maximum(-52/3 , 97556/27),Minimum(2,0)