Given the function g(x) = 6x3 + 27x2-72x, find the first derivative, g\'(x). g\'

Question

Given the function g(x) = 6x3 + 27x2-72x, find the first derivative, g'(x). g'(x) = Notice that g'(x)=0 when x = - 4 : that is: g'(-4) = 0. Now, we want to know whether there is a local minimum or local maximum at x = -4, so we will use the second derivative test. Find the second derivative, g"(x). g"(x) = Evaluate g"(-4). g"(-4)= Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x =-4? [Answer either up or down -- watch your spelling!!] At x = -4 the graph of g(x) is concave Based on the concavity of g(x) at x = -4, does this mean that there is a local minimum or local maximum at x = -4 ? [Answer either minimum or maximum -- watch your spelling!!] At x = -4 there is a local

Explanation / Answer

G'(x)=18x^2+54x-72 G"(x)=36x+54 G"(-4)=-90 at x=-4 concave downward x=-4 local maxima

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

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