# Math Help - Differentiable question

1. ## Differentiable question

One more question i find myself stuck at. Once again thanks in advance!

f(x)= { 2kx^2-x , x>3
x^3 +cx , x <(or equal to) 3

What is the value of k+c if the function is differentiable everywhere?

2. Originally Posted by painterchica16
One more question i find myself stuck at. Once again thanks in advance!

f(x)= { 2kx^2-x , x>3
x^3 +cx , x <(or equal to) 3

What is the value of k+c if the function is differentiable everywhere?
You need a smooth join at x = 3.

So f(x) is not allowed to have a jump discontinuity and f'(x) is not allowed to have a jump discontinuuity at x = 3.

So solve the following equations simultaneously:

$2k(3)^2 - 3 = (3)^3 + c(3)$ .... (1)

$4k(3) - 1 = 3 (3)^2 + c$ .... (2)