1. Consider the function g(x) = x3 +3x2 +1. (i) Find the derivative g (x) = ?? (ii) Factor the expression y found in (i) (iii) Now use (ii) to solve the equation: g (x) = 0 for x = ?? 2. (i) Next, on the number line below, mark the zeros you found in #1. E----- sign of g' (or ZERO) (ii) Now find an x-value between the two zeros. Determine whether g '(x) is positive or negative in that interval. Then mark the interval with the appropriate signs. The (iii) Now repeat (iii), for the portion of the line to the left of the interval you just marked. (iv) Finally, do the same for the portion of the line to the right of the interval from (ii). (v) We can now determine the local maxima / minima of g(x). Write their coordinates. (vi) Next, from your signs diagram, determine on which intervals g(x) is increasing (uphill) and decreasing (downhill). (vii) We now have enough information to draw the graph of g(x) = x3 +3x2 +1. So draw axes, and plot the points from (v). Then fill in the rest of the graph.
1. Consider the function g(x) = x3 +3x2 +1. (i) Find the derivative g (x) = ?? (ii) Factor the expression y found in (i) (iii) Now use (ii) to solve the equation: g (x) = 0 for x = ?? 2. (i) Next, on the number line below, mark the zeros you found in #1. E----- sign of g' (or ZERO) (ii) Now find an x-value between the two zeros. Determine whether g '(x) is positive or negative in that interval. Then mark the interval with the appropriate signs. The (iii) Now repeat (iii), for the portion of the line to the left of the interval you just marked. (iv) Finally, do the same for the portion of the line to the right of the interval from (ii). (v) We can now determine the local maxima / minima of g(x). Write their coordinates. (vi) Next, from your signs diagram, determine on which intervals g(x) is increasing (uphill) and decreasing (downhill). (vii) We now have enough information to draw the graph of g(x) = x3 +3x2 +1. So draw axes, and plot the points from (v). Then fill in the rest of the graph.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:1. Consider the function g(x) = x3 +3x2 +1.
(i) Find the derivative g (x) = ??
(ii) Factor the expression y found in (i)
(iii) Now use (ii) to solve the equation: g (x) = 0 for x = ??
2. (i) Next, on the number line below, mark the zeros you found in #1.
E----- sign of g' (or ZERO)
(ii) Now find an x-value between the two zeros. Determine whether g '(x) is positive
or negative in that interval. Then mark the interval with the appropriate signs. The
(iii) Now repeat (iii), for the portion of the line to the left of the interval you just
marked.
(iv) Finally, do the same for the portion of the line to the right of the interval from
(ii).
(v) We can now determine the local maxima / minima of g(x). Write their
coordinates.
(vi) Next, from your signs diagram, determine on which intervals g(x) is increasing
(uphill) and decreasing (downhill).
(vii) We now have enough information to draw the graph of g(x) = x3 +3x2 +1.
So draw axes, and plot the points from (v). Then fill in the rest of the graph.
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