Find all relative extrema and classify each as a maximum or minimum. Use the sec

Question

Find all relative extrema and classify each as a maximum or minimum. Use the second derivative f(x) = 5x^2+ 6x - 8 Select the correct choice below and, if necessary, fill in the answer box(es) to complete your The relative minima are and the relative maxima are (Simplify your answer. Use integers or fractions for any numbers in the expression. Type needed.) The relative minima are and there are no relative maxima. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type needed.) The relative maxima are and there are no relative minima. (Simplify your answer. Use integers or fractions for any numbers in the expression. Type needed.) There are no relative minima and there are no relative maxima.

Explanation / Answer

given f(x)=5x2+6x-8

differentiate with respect to x

f '(x)=10x+6

for critical number , f '(x)=0

10x+6=0

x=-3/5

f(-3/5)=5(-3/5)2+6(-3/5)-8

f(-3/5)=-49/5

critical point is (-3/5,-49/5)

f ''(x)=10

f "(-3/5)=10 >0

so relative minimum is -49/5 and no relative maxima

Related Questions

Navigate

• Browse (All)
• Browse F
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.