# What are the values and types of the critical points, if any, of #f(x)=7x^4-6x^2+1 #?

##### 1 Answer

#### Explanation:

Finding the critical values requires that

#f'(c)=0# , or#f'(c)# is undefined, and#c in # the domain of#f(x)#

Find the derivative of

Set

Factor the left hand side.

Divide both sides by 4 to simplify.

Solve each term in the product separately.

Determine the types of critical points by looking at the graph of

graph{7x^4-6x^2+1 [-1.3, 1.3, -0.5, 1.5]}

When

When

All three critical points **stationary** points because they have horizontal tangents at those critical points.