What is the extreme 36x^5+540x^4+2100x^3-30 ?

The extreme 36x^5+540x^4+2100x^3-30 is Maximum(-7,-28842),Minimum(-5,-37530),Saddle(0,-30)

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extreme 36x^5+540x^4+2100x^3-30

extreme points

36 x^{5} + 540 x^{4} + 2100 x^{3} - 30

Maximum (- 7, - 28842), Minimum (- 5, - 37530), Saddle (0, - 30)

Solution steps

f^{'} (x) = 180 x^{4} + 2160 x^{3} + 6300 x^{2}

Find intervals:

Increasing

: - \infty < x < - 7,

Decreasing

: - 7 < x < - 5,

Increasing

: - 5 < x < 0,

Increasing

: 0 < x < \infty

Plug

x = - 7

into

36 x^{5} + 540 x^{4} + 2100 x^{3} - 30 : - 28842

Maximum (- 7, - 28842)

Plug

x = - 5

into

36 x^{5} + 540 x^{4} + 2100 x^{3} - 30 : - 37530

Minimum (- 5, - 37530)

Plug

x = 0

into

36 x^{5} + 540 x^{4} + 2100 x^{3} - 30 : - 30

Saddle (0, - 30)

Maximum (- 7, - 28842), Minimum (- 5, - 37530), Saddle (0, - 30)

(x + 1) (x + 2) (x + 3) (x + 4)

y = (\frac{1}{x ^{2} - 4 x - 5})

f (x) = 5 cos (2 x)

f (x) = 340 x^{2} + 4080 x^{3}, 0 \leq x \leq 0.08

y = - x^{2} - 6 x - 8

What is the extreme 36x^5+540x^4+2100x^3-30 ?
The extreme 36x^5+540x^4+2100x^3-30 is Maximum(-7,-28842),Minimum(-5,-37530),Saddle(0,-30)