What is the extreme f(x)=2x^3+16x^2+32x+5 ?

The extreme f(x)=2x^3+16x^2+32x+5 is Maximum(-4,5),Minimum(-4/3 ,-377/27)

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extreme f(x)=2x^3+16x^2+32x+5

extreme points

f (x) = 2 x^{3} + 16 x^{2} + 32 x + 5

Maximum (- 4, 5), Minimum (- \frac{4}{3}, - \frac{377}{27})

Solution steps

f^{'} (x) = 6 x^{2} + 32 x + 32

Find intervals:

Increasing

: - \infty < x < - 4,

Decreasing

: - 4 < x < - \frac{4}{3},

Increasing

: - \frac{4}{3} < x < \infty

Plug

x = - 4

into

2 x^{3} + 16 x^{2} + 32 x + 5 : 5

Maximum (- 4, 5)

Plug

x = - \frac{4}{3}

into

2 x^{3} + 16 x^{2} + 32 x + 5 : - \frac{377}{27}

Minimum (- \frac{4}{3}, - \frac{377}{27})

Maximum (- 4, 5), Minimum (- \frac{4}{3}, - \frac{377}{27})

y = \frac{x + 5}{x ^{2} - 4}

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

f (x) = x^{2} - 16 x, - 4 \leq x \leq 4

f (x) = e^{x} (x + 4)

f (x) = (x - 4) (x + 1) (x + 4)

What is the extreme f(x)=2x^3+16x^2+32x+5 ?
The extreme f(x)=2x^3+16x^2+32x+5 is Maximum(-4,5),Minimum(-4/3 ,-377/27)