calc again!

posted by .

i got answers for this one, but i feel like i did something wrong.

2x+1 when x is less than or equal to 2
(1/2)x^2 + k when x is greater than 2

1) what value of k will make f continuous at x = 2?
my answer: i got k = 3 because it would make the two parts of the function match up at the point (2,5).
2) using that value of k, determine whether f is differentiable at x = 2.
my answer: i said yes because the derivatives of each part of the function are equal.
3) if k = 4, is f differentiable at x = 2?
my answer: no because it is not continuous at x =2 when k = 4.

  • calc again! -

    1) correct
    2) correct. At x=2, the 2x+1 curve has a slope of 2, and the (1/2)x^2 + 3 curve has a slope of x = x = 2 also. Therefore it is differentiable there.
    3) correct also. You cannot differentiate at a discontinuity, even if the slopes of the lines on each side are the same.

  • calc again! -

    thank you sososososo much! i was pretty sure of these, but i wanted to double-check.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. algebra

    20 - 4/5x greater than or equal to 16. I did this and got the answer x greater than or equal to -5 but the correct answer is said to be x is less than or equal to 5. i am not sure what i did wrong. thanks
  2. Calculus (Answer Check)

    Are my answers right? If they are wrong you don't have to tell me how to do it its okay =) A particle starts at time t=0 and moves along the x-axis so that its position at any time t(greater or equal to) 0 is given by x(t)=(t-1)^3
  3. i lied. very quick calc problem.

    f(x) = abs(sin(x)), -pi less than or equal to x less than or equal to pi g(x) = x^2 let H(x) = g(f(x)) i got that H(x) would equal sin^2(x). THIS IS WHERE I AM STUCK! find the domain of H. do i still need to account for "-pi less than …
  4. Algebra--Correction?

    Solve x^2 -3x is greater than or equal to 10 Would the solutions be x=5 and x= -2?
  5. Math

    I'm having a hard time with graphing this problem. Could someone please help?
  6. Rational Inequality with Absolute Value

    Here's a question I'm having trouble with: |x|/|x+2|<2 Solve for x. I'm trying to use the case method to solve this problem. Basically I just need confirmation that I did this correctly. I'm doing this through distance learning …
  7. math

    State the null hypothesis, Ho, and the alternative hypothesis, Ha, that would be used to test the following statements. (a) The linear correlation coefficient is positive. Ho: ñ ---Select--- not equal to equal to greater than less …
  8. Math

    Hi everyone, my name is Emerson. I was wondering if anybody could help me on a test. I'm stuck on some, but I think I know some others. Thank you! 1. Translate the phrase "nine more than two times a number" in to an algebraic expression. …
  9. math

    7. The tennis team is selling key chains as a fundraiser. If its goal is to raise is at least 180, how many key chains must it sell at $2.25 each to meet that goal?
  10. Pre calc quick question

    if a problem says f(x)=square root x^2-16; x less than or equal to -4. Find domain and range. to do this i set up the equation like x^2-16 less than or equal to -4. However by doing this I am runnning into complications findng domain …

More Similar Questions