# What is the condition for two extreme points?

I am new to the topic of extreme point and trying to get the whole picture. Now I know the extreme theorm that mentions two condition to obtain a critical points what are $$f'(x)= 0$$ or $$f'(x)=$$ undefined.

I solved some examples of those on Khan Academy but coming across this example $$mathrm{Let} , a,b,c,d, in , mathbb{R}, aneq0, f: mathbb{R} longrightarrow mathbb{R}, f(x)=a,x^3 + b ,x^2 + c, x + d.$$

• (a) What is the condition for two extreme points?
• the answer supposed to be (a) $$,b^2>3ac$$.

Can I know how and which topic this fall into?

Mathematics Asked by Mai Ehab on November 14, 2021

if you calculate de $$f'(x) = 0$$, you will see the condition for the "square root" to be positive (you fall into a quadratic equation), is $$sqrt{(b^2 - 3ac)},$$ so, to be positive, you'll need $$b^2 > 3ac.$$ After this you can exploit the signals of $$a$$ and $$c$$, if you want it.

Answered by Bruno on November 14, 2021

## Related Questions

### Nimber multiplication

2  Asked on July 30, 2020 by yberman

### What is the radius of convergence of $a_n$ where $a_{n+1}=frac{n-5}{n+1}a_n$?

2  Asked on July 28, 2020 by lucas

### Discretization formula for a system of two differential equations. “Solution to one of these is the initial condition of the other”. In which sense?

0  Asked on July 27, 2020 by strictly_increasing

### Calculating distance when velocity is given

1  Asked on July 27, 2020 by aruha

### dimension of intersection of subspaces, one of which of dimension $n-1$

1  Asked on July 27, 2020 by gulzar

### Let $A$ be a subset of $mathbb{R}$ such that $A$ is bounded below with inf $A = L > 0$.

2  Asked on July 26, 2020 by outlier