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Find the critical values for f(x) = \frac{3x^2}{9-x^2}

Question:

Find the critical values for {eq}f(x) = \frac{3x^2}{9-x^2} {/eq}

Critical Points:


For a function defined in the cartesian plane, the set of points for which the function's value turns out to be zero or undefined, such points are known as the Critical points of that function. These points help to determine the extrema of the function.

Answer and Explanation:


Given: {eq}f(x) = \dfrac{3x^2}{9-x^2} {/eq}

{eq}\Rightarrow f'(x)=\dfrac{6x(9-x^2)+(2x)3x^2}{(9-x^2)^2}=\dfrac{54x}{(x^2-9)^2} {/eq}

As we know that the critical points are the points where the function's value is zero or the function is undefined.

Hence, the critical points will be {eq}x=0,\pm 3. {/eq}


Learn more about this topic:

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Finding Critical Points in Calculus: Function & Graph

from CAHSEE Math Exam: Tutoring Solution

Chapter 8 / Lesson 9
203K

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