calc again!
posted by jane .
i got answers for this one, but i feel like i did something wrong.
f(x)=
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.

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. 
thank you sososososo much! i was pretty sure of these, but i wanted to doublecheck.
Respond to this Question
Similar Questions

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 
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 xaxis so that its position at any time t(greater or equal to) 0 is given by x(t)=(t1)^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 … 
AlgebraCorrection?
Solve x^2 3x is greater than or equal to 10 Would the solutions be x=5 and x= 2? 
Math
I'm having a hard time with graphing this problem. Could someone please help? 
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 … 
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 … 
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. … 
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? 
Pre calc quick question
if a problem says f(x)=square root x^216; x less than or equal to 4. Find domain and range. to do this i set up the equation like x^216 less than or equal to 4. However by doing this I am runnning into complications findng domain …