Determine the maximum or minimum value of the following quadratic function. LaTeX: f\left(x\right)=-3\left(x+5\right)^2-1f ( x ) = − 3 ( x + 5 ) 2 − 1

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asked Oct 25, 2022 178k views

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Determine the maximum or minimum value of the following quadratic function. LaTeX: f\left(x\right)=-3\left(x+5\right)^2-1f ( x ) = − 3 ( x + 5 ) 2 − 1

Mathematics
high-school

Vito De Tullio asked

by Vito De Tullio

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Answer:

Explanation:

$y=-3(x^2+10x+25)-1\\ \\ y=-3x^2-30x-76\\ \\ dy=-6x-30\\ \\ d^2y=-6\\ \\ \text{Since the second derivative is always negative, when the first derivative is equal to zero the function will be at a global maximum.}\\ \\ dy=0=-6x-30\\ \\ x=-5\\ \\ f(-5)=-1\\ \\ \text{So the global maximum occurs at the point (-5,-1)$

Rob Potter answered Nov 1, 2022

by Rob Potter

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