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

The extreme f(x)=(x^4)/4-x^3+3 is Saddle(0,3),Minimum(3,-15/4)

Popular >

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

extreme points

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

Saddle (0, 3), Minimum (3, - \frac{15}{4})

Solution steps

f^{'} (x) = x^{3} - 3 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

\frac{x ^{4}}{4} - x^{3} + 3 : 3

Saddle (0, 3)

Plug

x = 3

into

\frac{x ^{4}}{4} - x^{3} + 3 : - \frac{15}{4}

Minimum (3, - \frac{15}{4})

Saddle (0, 3), Minimum (3, - \frac{15}{4})

f (x) = - 3 (x + 2) e^{4 x}, (- 5, 0)

sin (5 x), - \frac{π}{5} \leq x \leq \frac{π}{4}

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

f (x) = 0.5 x^{2} + 15 x + 5000

f (x) = \frac{x ^{5}}{20} - 1 x^{3}

What is the extreme f(x)=(x^4)/4-x^3+3 ?
The extreme f(x)=(x^4)/4-x^3+3 is Saddle(0,3),Minimum(3,-15/4)