Question

help me with these problems and ill give you amazing ratings!! (must do all please)

11. Make a detailed graph of the function f)-1---on the interval |-4,1] by completing the following steps (a) Compate f(x). (Make sure it is correct before contisuing) (b) Determine those points a Determine those points x for which f(e)-o, that is, compate the eritical pointa of (oeparate multiple points with commas) answer in the form of a sign chart for ) You will lose credit if your anaseer is not in the form of a sign chart. (c) Determine the iatervals on which f(a)> 0 and the intervals on which f(a)0. Display your (d) Using your answer in (e), which of the points are local mazima and local minima of f(x). (separate multiple points by commas) (separate multiple points by commas) local minima: local maxima:z- (e) Compute /"(e). (Reler to your answer in part (o)) a) (1) Determine those points a for which f"(x) comma) (separate multiple points with エーーーーー ーーーーーーーー (g) Determine the intervals on which f"(z) > 0 and the intervals on which f"(z) < 0, Display your answer in the form of a sign chart for f"(x). 10

Answer 1

f(r) = 1-9-r-622-23 Find the critical points: 2 dx 0-9. 1-6. 2x2-1 -3r3-1 0-9-12r-3r f(x)-3r2-12r-9

b)

Solve-32.2-12x-9 0 (12)-12)-4(-3) -9) 2 (-3) : T1, 2 1236 -2-3 12±6 6

c)

Check the sign of 3r2-12r - 9 at -4 <<-3: Evaluate the derivative at a point on the interval. Take the point-4 and plug it into - 322-9 3 (-4)- 12 (-4) 9 9 <0 Check the sign of-3r- 12r - 9 at -3 < <-1 Evaluate the derivative at a point on the interval. Take the point-2 and plug it into - 322-9 3 (-2) - 12 (-2) - 9 3 > 0 Check the sign of -312-12r -9at -1<<1 Evaluate the derivative at a point on the interval. Take the point r0 and plug it into- 3a2 12x-9 3. 02- 12.0-9

	-4<x<-3	-3<x<-1	-1<x<1
Sign	-	+	-
Behaviour	Decreasing	Increasing	Decreasing

d)

local Maximum 2,--1,-4 local Minimum x=-3. 1