Wednesday

July 23, 2014

July 23, 2014

Posted by **Lin** on Sunday, April 1, 2012 at 12:10pm.

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.

**Related Questions**

Math--Calculus - I'm having a tough time figuring out this problem... S(x) = ...

calculus - Let f be the function defined by f(x)= sqrt(x), 0 <or= x <or= 4...

Calculus - Decide if the following function f(x) is differentiable at x=0. Try ...

calculus - In the following problem, suppose f(x) is continuous (and ...

Calculus - 1. For a differentiable function f, f' be the funcyion defined by f'(...

Calculus - Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero ...

Calculus - I need help creating an equation for a piecewise defined function ...

Calculus - Let f be a twice-differentiable function such that f(2)=5 and f(5)=2...

Calculus - Assuming that f and g are functions differentiable at a (though we do...

Calculus - Determine whether Rolle's Theorem can be applied to f on the closed ...