# How do you find intercepts, extrema, points of inflections, asymptotes and graph #f(x)=(4x)/(sqrt(x^2+15))#?

##### 1 Answer

Jan 16, 2017

No intercepts. Horizontal asymptotes :

Point of inflexion : O ( see the graph ),

No extrema, as

#### Explanation:

Use

If (x, y) is on the graph, so is (-x, -y), showing symmetry about O.

As

Cross multiply and differentiate to get the following results.

y' simplifies to

y, y and y''. vanish at O and

graph{(4x/sqrt(x^2+15)-y)(y+4)(y-4)=0 [-10, 10, -5, 5]}