What is the extreme f(x)=7x^3(x+1)^2 ?

The extreme f(x)=7x^3(x+1)^2 is Maximum(-1,0),Minimum(-3/5 ,-756/3125),Saddle(0,0)

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extreme f(x)=7x^3(x+1)^2

extreme points

f (x) = 7 x^{3} (x + 1)^{2}

Maximum (- 1, 0), Minimum (- \frac{3}{5}, - \frac{756}{3125}), Saddle (0, 0)

Solution steps

f^{'} (x) = 7 (5 x^{4} + 8 x^{3} + 3 x^{2})

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < - \frac{3}{5},

Increasing

: - \frac{3}{5} < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 1

into

7 x^{3} (x + 1)^{2} : 0

Maximum (- 1, 0)

Plug

x = - \frac{3}{5}

into

7 x^{3} (x + 1)^{2} : - \frac{756}{3125}

Minimum (- \frac{3}{5}, - \frac{756}{3125})

Plug

x = 0

into

7 x^{3} (x + 1)^{2} : 0

Saddle (0, 0)

Maximum (- 1, 0), Minimum (- \frac{3}{5}, - \frac{756}{3125}), Saddle (0, 0)

y = 17 x^{4} - 102 x^{2}

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

f (x) = [24144]

f (x) = x^{4} - 2 x^{2} + 8, - 4 \leq x \leq 4

16 x^{4} + 125 x

What is the extreme f(x)=7x^3(x+1)^2 ?
The extreme f(x)=7x^3(x+1)^2 is Maximum(-1,0),Minimum(-3/5 ,-756/3125),Saddle(0,0)