February 25, 2017

Homework Help: calc again!

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.

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.

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