Asked by Jeff
Use the information in the image: imgur(.)com/a/YzAGLvs (Remove the parenthesis to use link)
1. On what interval is g increasing? Justify your answer.
2. For 0 ≤ x ≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
1. On what interval is g increasing? Justify your answer.
2. For 0 ≤ x ≤ 6, express g(x) in terms of x. Do not include +C in your final answer.
Answers
Answered by
Steve
g is increasing when g' > 0
g'(x) = f(x)
f(x) > 0 when -3 < x < 6
g(x) = ∫[-2,x] 3 dt = 3t [-2,x] = -6-3x for -3<=x<0
g(x) = ∫[-2,x] 3-t dt = 3t - t^2/2 [-2,x] = x^2/2 - 3x - 8 for 0<=x<=6
g(x) = ∫[-2,x] -3 dt = -3t [-2,x] = 6-3x for 6<x<=9
g'(x) = f(x)
f(x) > 0 when -3 < x < 6
g(x) = ∫[-2,x] 3 dt = 3t [-2,x] = -6-3x for -3<=x<0
g(x) = ∫[-2,x] 3-t dt = 3t - t^2/2 [-2,x] = x^2/2 - 3x - 8 for 0<=x<=6
g(x) = ∫[-2,x] -3 dt = -3t [-2,x] = 6-3x for 6<x<=9
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.