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elena55 [62]
3 years ago
14

At what value(s) of x does f(x)=x^4-18x^2 have a critical point where the graph changes from decreasing to increasing?

Mathematics
2 answers:
My name is Ann [436]3 years ago
6 0
Take f"(x)=0 to find critical values v1,v2,...
take f (vn)
produces inflection points
Yanka [14]3 years ago
4 0

Answer:

x = 2, x = -2 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:

f(x) = x^4 - 18x^2

We have to find the critical points of the given expression.

First we differentiate the given expression with respect to x.

\displaystyle\frac{d(f(x))}{dx} = 4x^3 - 16x

Equating f'(x) to zero, to obtain the critical points:

f'(x) = 0\\4x^3 - 16x = 0\\x(4x^2 - 16) = 0\\x(2x-4)(2x+4) = 0\\x = 0, x = 2, x = -2

Hence, x = 2, x = -2 are the critical points where the graph changes from decreasing to increasing.

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