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.