What is the extreme f(x)=6x^5-2x^4 ?

The extreme f(x)=6x^5-2x^4 is Maximum(0,0),Minimum(4/15 ,-512/253125)

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extreme f(x)=6x^5-2x^4

extreme points

f (x) = 6 x^{5} - 2 x^{4}

Maximum (0, 0), Minimum (\frac{4}{15}, - \frac{512}{253125})

Solution steps

f^{'} (x) = 30 x^{4} - 8 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{4}{15},

Increasing

: \frac{4}{15} < x < \infty

Plug

x = 0

into

6 x^{5} - 2 x^{4} : 0

Maximum (0, 0)

Plug

x = \frac{4}{15}

into

6 x^{5} - 2 x^{4} : - \frac{512}{253125}

Minimum (\frac{4}{15}, - \frac{512}{253125})

Maximum (0, 0), Minimum (\frac{4}{15}, - \frac{512}{253125})

f (x) = - x^{3} + 3 x^{2} + 2880 x - 500

x^{3} - 3 x^{2} - 9 x + 10

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

f (x) = x - sin (- x)

y = x x - 6

What is the extreme f(x)=6x^5-2x^4 ?
The extreme f(x)=6x^5-2x^4 is Maximum(0,0),Minimum(4/15 ,-512/253125)