What is the extreme 5x^5-3x^4+2 ?

The extreme 5x^5-3x^4+2 is Maximum(0,2),Minimum(12/25 , 3844042/1953125)

extreme 5x^5-3x^4+2

extreme points

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

Maximum (0, 2), Minimum (\frac{12}{25}, \frac{3844042}{1953125})

Solution steps

f^{'} (x) = 25 x^{4} - 12 x^{3}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{12}{25},

Increasing

: \frac{12}{25} < x < \infty

Plug

x = 0

into

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

Maximum (0, 2)

Plug

x = \frac{12}{25}

into

5 x^{5} - 3 x^{4} + 2 : \frac{3844042}{1953125}

Minimum (\frac{12}{25}, \frac{3844042}{1953125})

Maximum (0, 2), Minimum (\frac{12}{25}, \frac{3844042}{1953125})

f (x) = 4 - x, - 3 \leq x \leq 3

f (x, y) = (x^{2} - 9)^{2} + (y^{2} - 36)^{2}

f (x) = - 3 x^{2} - 12 x + 24 y^{2} + 12 y = 0

f (x) = 7 x - 5

ln (x) - 7 x + 11

What is the extreme 5x^5-3x^4+2 ?
The extreme 5x^5-3x^4+2 is Maximum(0,2),Minimum(12/25 , 3844042/1953125)