Answer :
take f"(x)=0 to find critical values v1,v2,...
take f (vn)
produces inflection points
take f (vn)
produces inflection points
Answer:
[tex] x = 2, x = -2[/tex] are the critical points where the graph changes from decreasing to increasing.
Step-by-step explanation:
- Critical points are the points on the where the function either a changes from increasing to decreasing or from decreasing to increasing.
- Critical points are useful for determining maxima, minima and solving optimization problems.
We are given the expression:
[tex]f(x) = x^4 - 18x^2[/tex]
We have to find the critical points of the given expression.
First we differentiate the given expression with respect to x.
[tex]\displaystyle\frac{d(f(x))}{dx} = 4x^3 - 16x[/tex]
Equating f'(x) to zero, to obtain the critical points:
[tex]f'(x) = 0\\4x^3 - 16x = 0\\x(4x^2 - 16) = 0\\x(2x-4)(2x+4) = 0\\x = 0, x = 2, x = -2[/tex]
Hence, [tex] x = 2, x = -2[/tex] are the critical points where the graph changes from decreasing to increasing.