Home > Calculus > Classifying Critical Points and Extreme Values for a Function

How do you find the extreme values of the function and where they occur?

Answer 1

See below.

To find extreme values of a function #f#, set #f'(x)=0# and solve. This gives you the x-coordinates of the extreme values/ local maxs and mins.

For example. consider #f(x)=x^2-6x+5#. To find the minimum value of #f# (we know it's minimum because the parabola opens upward), we set #f'(x)=2x-6=0# Solving, we get #x=3# is the location of the minimum. To find the y-coordinate, we find #f(3)=-4#. Therefore, the extreme minimum of #f# occurs at the point #(3,-4)#.

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Answer 2

Cameron Alexander

To find the extreme values of a function, you first find its critical points by setting the derivative equal to zero and solving for x. Then, you evaluate the function at these critical points and at the endpoints of the domain (if applicable). The highest and lowest function values are the maximum and minimum values, respectively, and they occur at the corresponding critical points or endpoints.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.