Please check my Calculus

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

  1. 👍 0
  2. 👎 0
  3. 👁 171
  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?

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

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. calc

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. f(x)= x sqrt(x+21) , [-21,0] If there is more than one

    asked by Jossy on April 12, 2007
  2. calculus

    Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the three hypotheses of Rolle’s theorem on the interval [0,3]. Then find the values of c on the interval [0,3] that are guaranteed by Rolle’s theorem. Give your answer as

    asked by esma on October 6, 2010
  3. calc

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's

    asked by Julia on April 14, 2007
  4. URGENT!! PLEASE Calc

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers "c" that satisfy the conclusion of Rolle's Theorem. f(x)=sin4pix , [-1/2,1/2] Well according to Rolle's

    asked by Julia on April 14, 2007
  5. math

    Verify that the function f(x)=x^3-6x^2+8x+4 satisfies the three hypotheses of Rolle's Theorem on the given interval [0,4]. Then find all numbers c that satisfy the conclusion of Rolle's Theorem

    asked by Kay on June 1, 2013
  6. Math

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. (Select all that apply.) f (x) = sin(x), [0, 2π] If Rolle's Theorem can be applied, find all values of c in the open interval (a, b) such that f

    asked by Angelina on March 7, 2012
  7. Calculus

    Determine whether Rolle's Theorem can be applied to f on the closed interval [a,b]. If Rolle's Theorem can be applied, find all values of c in the open interval (a,b) such that f'(x)=0. f(x) = x^(2/3) - 1 [-8,8] I plugged in both

    asked by Maddie on September 26, 2013
  8. calc

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = x^3

    asked by sam on March 26, 2015
  9. Calculus 1

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) =

    asked by TayB on October 24, 2015
  10. Calculus

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) =

    asked by Anonymous on May 11, 2018
  11. math

    Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. (Enter your answers as a comma-separated list.) f(x) = 5 −

    asked by sara on March 23, 2015

More Similar Questions