Asked by Lin
Suppose f(x) is a differentiable function with f(-1)=2 and f(2)=-1. The differentiable function g(x) is defined by the formula g(x)=f(f(x))'
A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 and 2.
B. Compute g'(-1) and g'(2) in terms of values of f and f'. Verify that g'(-1) = g'(2). Explain why g"(x)=0 must have at least one solution B between -1 and 2.
C. Suppose now that f(x)=Cx^2 +D. Find values of C and D so that f(-1)=2 and f(2)=-1. Compute g(x)=f(f(x)) directly for those values of C and D and use algebra on the resulting formulas for g(x) and g"(x) to find numbers A and B between -1 and 2 so that g(A)=0 and g"(B)=0. The "abstract" assertions of a) and b) should be verified.
A. Compute g(-1) and g(2). Explain why g(x)=0 must have at least one solution A between -1 and 2.
B. Compute g'(-1) and g'(2) in terms of values of f and f'. Verify that g'(-1) = g'(2). Explain why g"(x)=0 must have at least one solution B between -1 and 2.
C. Suppose now that f(x)=Cx^2 +D. Find values of C and D so that f(-1)=2 and f(2)=-1. Compute g(x)=f(f(x)) directly for those values of C and D and use algebra on the resulting formulas for g(x) and g"(x) to find numbers A and B between -1 and 2 so that g(A)=0 and g"(B)=0. The "abstract" assertions of a) and b) should be verified.
Answers
There are no human answers yet.
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.