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Popular >

extreme 3x^5-5x^3+2

Solution

extreme points

3 x^{5} - 5 x^{3} + 2

Solution

Maximum (- 1, 4), Saddle (0, 2), Minimum (1, 0)

Solution steps

f^{'} (x) = 15 x^{4} - 15 x^{2}

Find intervals:

Increasing

: - \infty < x < - 1,

Decreasing

: - 1 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 1

into

3 x^{5} - 5 x^{3} + 2 : 4

Maximum (- 1, 4)

Plug

x = 0

into

3 x^{5} - 5 x^{3} + 2 : 2

Saddle (0, 2)

Plug

x = 1

into

3 x^{5} - 5 x^{3} + 2 : 0

Minimum (1, 0)

Maximum (- 1, 4), Saddle (0, 2), Minimum (1, 0)

Popular Examples

extreme y=e^{-4t}+e^{-5t}extreme points

y = e^{- 4 t} + e^{- 5 t}

extreme f(x)=(2x)/(x^4+1)extreme points

f (x) = \frac{2 x}{x ^{4} + 1}

extreme f(x)=3x-ln(3x),(0,4)extreme points

f (x) = 3 x - ln (3 x), (0, 4)

extreme 2x^3-9x extreme points

2 x^{3} - 9 x

extreme f(x)=(2x^3-3x^2-12x+1)extreme points

f (x) = (2 x^{3} - 3 x^{2} - 12 x + 1)

Frequently Asked Questions (FAQ)

What is the extreme 3x^5-5x^3+2 ?
The extreme 3x^5-5x^3+2 is Maximum(-1,4),Saddle(0,2),Minimum(1,0)