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Find the relative extrema of the function and classify each as a maximum or minimum. s(x) = -x2 - 6x + 112 Relative maximum: (-6, 112) Relative maximum:(-3, 121) Relative maximum: (3, 121) Relative minimum: (6, 112)

Find The Relative Extrema Of The Function And Classify Each As A Maximum Or Minimum Sx X2 6x 112 Relative Maximum 6 112 Relative Maximum3 121 Relative Maximum 3 class=

Sagot :

To find the relative extrema of the function

[tex]s(x)=-x^2-6x+112[/tex]

We need to find the derivative of the function, then

[tex]\frac{ds}{dx}=-2x-6[/tex]

Then we equate the derivative to zero and solve for x:

[tex]\begin{gathered} \frac{ds}{dx}=0 \\ -2x-6=0 \\ -2x=6 \\ x=-\frac{6}{2} \\ x=-3 \end{gathered}[/tex]

Therefore we have a relative extrema at x=-3 with value s=121.

Now we need to find out if this value is a maximum or minimum, to do that we need to find the derivative of the derivative.

[tex]\begin{gathered} \frac{d}{dx}(\frac{ds}{dx})=\frac{d}{dx}(-2x-6) \\ =-2 \end{gathered}[/tex]

Since the value of the second derivative is negative for every value of x, the relative extrema is a maximum.

Therefore we have a maximum at the point (-3,121).

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