Need help with part D and E please the last two questions The Second Derivative Test:Given the function g(x) = 8x° + 36x? + 48xA) Find the first derivative, g'(x).g'(x) =Notice that g'(x) = 0 when x =– 1. That is, g'( – 1) = 0.– 1, so we will useNow, we want to know whether there is a local minimum or local maximum at x =the second derivative test.B) Find the second derivative, g''(x).= (x),,6C) Evaluate g''(– 1).-g'"(– 1) =D) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at- 1At x- 1 the graph of g(x) is concave- Answer either up or down --||watch your spelling!!E) Based on the concavity of g(x) at x =- 1?- 1, does this mean that there is a local minimum or localmaximum at x =At x =- 1 there is a local- [Answer either min or maxwatch your--spelling!!]

D) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = - 1 At x = - 1 the graph of g(x) is concave - Answer either up or down -- watch your spelling!! E) Based on the concavity of g(x) at x = - 1, does this mean that there is a local minimum or local maximum at x = 1? At x = – 1 there is a local [Answer either min or max -- watch your spelling!!]

D) Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at x = - 1 At x = - 1 the graph of g(x) is concave - Answer either up or down -- watch your spelling!! E) Based on the concavity of g(x) at x = - 1, does this mean that there is a local minimum or local maximum at x = 1? At x = – 1 there is a local [Answer either min or max -- watch your spelling!!]

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.4: Combining And Decomposing Functions

Problem 14E: Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and...

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
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A function f has derivative f′(x)=x^3(x−1)^2(x+1)(x−2). At what numbers x, if any, does f have a local maximum? A local minimum?
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Consider a differentiable function f with domain R and derivativesf'(x)=-aebx(1+bx) and f"(x)=-abebx(2+bx) , with a and b nonzero real numbers.The function has only one critical point x=-1/b and a local maximum at x=-1/bUse the Second Derivative test to find the value(s) of a and b