Homework Help: Math/Calculus

Posted by Kate on Tuesday, September 9, 2008 at 10:09pm.

Find k so that the following function is continuous on any interval:

f(x)= kx
0 (less than or equal to) x (less than) 2

3x^2
2 (less than or equal to x)

i know the answer is 12 but i don't know how to arrive at that. could you please walk me through the steps? thanks.

Math/Calculus - drwls, Wednesday, September 10, 2008 at 4:17am
kx and 3x^2 are continuous where they apply. What you have to to is make sure they both give the same value at x=2, where one functional form changes to the other.

Thus require that 3x^2 = kx at x = 2.

3*4 = 2k

k = 6. The value of the function at x=2 is 12.

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