What is the extreme f(x)=x^5-3x^4+2 ?

The extreme f(x)=x^5-3x^4+2 is Maximum(0,2),Minimum(12/5 ,-55958/3125)

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extreme f(x)=x^5-3x^4+2

extreme points

f (x) = x^{5} - 3 x^{4} + 2

Maximum (0, 2), Minimum (\frac{12}{5}, - \frac{55958}{3125})

Solution steps

f^{'} (x) = 5 x^{4} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{12}{5},

Increasing

: \frac{12}{5} < x < \infty

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = \frac{12}{5}

into

x^{5} - 3 x^{4} + 2 : - \frac{55958}{3125}

Minimum (\frac{12}{5}, - \frac{55958}{3125})

Maximum (0, 2), Minimum (\frac{12}{5}, - \frac{55958}{3125})

f (x) = - x^{2} - 7 y^{2} + 9 x - 6 y + 2

\frac{3 x}{x - 8}

2 x^{3} - 1

2 x^{2} + 20 x - 6

x^{\frac{2}{5}}

What is the extreme f(x)=x^5-3x^4+2 ?
The extreme f(x)=x^5-3x^4+2 is Maximum(0,2),Minimum(12/5 ,-55958/3125)