Posted by **jane** on Friday, February 20, 2009 at 12:04am.

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.

- calc again! -
**drwls**, Friday, February 20, 2009 at 12:15am
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! -
**jane**, Friday, February 20, 2009 at 12:20am
thank you sososososo much! i was pretty sure of these, but i wanted to double-check.

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