Find all relative extrema and classify each as a maximum or minimum. f(x) = 5x^2

Question

Find all relative extrema and classify each as a maximum or minimum. f(x) = 5x^2 + 8x - 5 Select the correct choice below and, if necessary, fill in the answer box(es) The relative minima are and the relative maxima are. (Simplify your answer. Use integers or fractions for any numbers in needed.) The relative minima are and there are no relative maxima. (Simplify your answer. Use integers or fractions for any numbers in the needed.) The relative maxima are and there are no relative minima. (Simplify your answer. Use integers or fractions for any numbers in the needed.) There are no relative minima and there are no relative maxima.

Explanation / Answer

given f(x)=5x2+8x-5

differentiate with respect to x

f '(x)=10x+8

for critical number , f '(x)=0

10x+8=0

x=-8/10

x=-4/5

f(-4/5)=5(-4/5)2+8(-4/5)-5

f(-4/5)=(16/5)+(-32/5)-5

f(-4/5)=-41/5

critical point is (-4/5,-41/5)

f ''(x)=10

f "(-4/5)=10 >0

so relative minimum is -41/5 and no relative maxima

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