Home > Calculus > Identifying Turning Points (Local Extrema) for a Function

Given the function #y=2-x^2#, how do you determine the relative maximum or the relative minimum?

Answer 1

You set the derivative to zero. If the sign before the #x^2# is a minus (which it is), we search for a maximum (a "mountain" parabola)

#y'=-2x=0->x=0#

Fill in for #y#: #y(0)=2-0^2=2#

Maximum is at #(0,2)# graph{2-x^2 [-10, 10, -5, 5]}

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Answer 2

Samantha Adkison

To determine the relative maximum or minimum of the function ( y = 2 - x^2 ), you need to find the critical points by taking the derivative of the function, setting it equal to zero, and solving for ( x ). Then, you classify these critical points by examining the sign of the second derivative at each point. If the second derivative is positive, it indicates a relative minimum; if it's negative, it indicates a relative maximum. If the second derivative is zero or undefined, the test is inconclusive, and other methods may be needed to determine the nature of the critical point.

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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.