What is the extreme f(x)= 4/3 x^3-25/2 x^2+6x+4 ?

The extreme f(x)= 4/3 x^3-25/2 x^2+6x+4 is Maximum(1/4 , 455/96),Minimum(6,-122)

Popular >

extreme f(x)= 4/3 x^3-25/2 x^2+6x+4

extreme points

f (x) = \frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4

Maximum (\frac{1}{4}, \frac{455}{96}), Minimum (6, - 122)

Solution steps

f^{'} (x) = 4 x^{2} - 25 x + 6

Find intervals:

Increasing

: - \infty < x < \frac{1}{4},

Decreasing

: \frac{1}{4} < x < 6,

Increasing

: 6 < x < \infty

Plug

x = \frac{1}{4}

into

\frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4 : \frac{455}{96}

Maximum (\frac{1}{4}, \frac{455}{96})

Plug

x = 6

into

\frac{4}{3} x^{3} - \frac{25}{2} x^{2} + 6 x + 4 : - 122

Minimum (6, - 122)

Maximum (\frac{1}{4}, \frac{455}{96}), Minimum (6, - 122)

f (x y) = x^{2} y - 15 x y^{2} + 12 y

f (x) = 12 x^{2} - 18 x

- 6 x^{5} + 180 x^{3} - 1350 x + 14

ln (1 - 3 x)

ln (3 x^{2} + 12)

What is the extreme f(x)= 4/3 x^3-25/2 x^2+6x+4 ?
The extreme f(x)= 4/3 x^3-25/2 x^2+6x+4 is Maximum(1/4 , 455/96),Minimum(6,-122)