1. Find the value(s) of c guaranteed by Rolle’s Theorem for f(x)=x^2+3x on [0, 2]

Question

A. c=-3/2
B. c=0, 3
C. Rolle’s Theorem doesn’t apply as f is not continuous on [0, 2]
D. Rolle’s Theorem doesn’t apply as f(0) does not equal f(2)
E. None of these
I got D. I plugged in 0 and 2 into the function to see if they equalled and they didn't.

2. Determine the open intervals where the graph of f(x)=-1/(x+1)^2 is concave up or concave down.
A. concave down (negative infinity, infinity)
B. concave down (negative infinity, -1); concave up (-1, infinity)
C. concave down (negative infinity, -1) and (-1, infinity)
D. concave up (negative infinity, -1) and (-1, infinity)
E. none of these
I got C. I found the first derivative. I found the second derivative I used the interval test to determine concavity.

3. Consider f(x)=x^2/(x^2+a), a>0. Determine the effect on the graph of f if a is varied.
A. Each y value is multiplied by a
B. As a increases, the vertical tangent lines move further from the origin
C. The graph of the curve is shifted sqrt(a) units to the left.
D. As a increases, the curve approaches its asymptote more slowly
E. None of these
I think I asked this problem earlier but I'm still confused. Is there a way to figure this out with out a graph?

Answer 1

1,2 correct.

3. divide numerator and denominator by x^2

f(x)=1/(1+a/x^2)

consider a=1, and a= 6000. What does that do to the graph?

Answer 2

I don't know if you will see this but Is number 3's answer D?