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

The extreme f(x)=2x^5-6x^4 is Maximum(0,0),Minimum(12/5 ,-124416/3125)

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

extreme points

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

Maximum (0, 0), Minimum (\frac{12}{5}, - \frac{124416}{3125})

Solution steps

f^{'} (x) = 10 x^{4} - 24 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

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

Increasing

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

Plug

x = 0

into

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

Maximum (0, 0)

Plug

x = \frac{12}{5}

into

2 x^{5} - 6 x^{4} : - \frac{124416}{3125}

Minimum (\frac{12}{5}, - \frac{124416}{3125})

Maximum (0, 0), Minimum (\frac{12}{5}, - \frac{124416}{3125})

f (x) = x^{2} - 10 x + 24

f (x) = 2 x + \frac{300000}{x}, 1 \leq x \leq 300

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

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

\frac{1}{3} x^{3} - x^{2} + x - 5

What is the extreme f(x)=2x^5-6x^4 ?
The extreme f(x)=2x^5-6x^4 is Maximum(0,0),Minimum(12/5 ,-124416/3125)