Tuesday

September 30, 2014

September 30, 2014

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

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 12:15am1) 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 12:20amthank you sososososo much! i was pretty sure of these, but i wanted to double-check.

**Answer this Question**

**Related Questions**

i lied. very quick calc problem. - f(x) = abs(sin(x)), -pi less than or equal to...

Math - Solve the inequality: 2x-1 / 3x-2 < 1 [the < is actually less than ...

calc ii - if we know that 12 is less than or equal to f(x) which is less than or...

Calculus - Hey there. I have a quick question. Ive done questions like these ...

calculus - Consider the function f(x)=(x^3)(e^9x), -2 is less than or equal to x...

ap stats - Continuous Random Variable, I Let X be a random number between 0 and ...

stats - Continuous Random Variable, I Let X be a random number between 0 and 1 ...

pre calc - Solve: (x+5/x)+(6/x-4)=(-7/x^2-4x) I multiplied the entire function ...

Algebra - Hi! I was wondering if anyone might be willing to check my answers for...

Pre Calc still confused - Solve: (x+5/x)+(6/x-4)=(-7/x^2-4x) I multiplied the ...