Is it possible to choose k so that the following function is continuous and differentiable at x = -3?
f(x) = (2x^2 - 18)/(x+3) if x does not equal to -3
k if x = -3
For continuous I'm thinking k = -12 because f(-3) must equal k and the limit as x approaches -3 is -12.
I'm having trouble with differentiable though. The derivative of f(x) is 2, and if k = 2, then the derivative of that is zero, so is it not differentiable?
Thanks.
f(x) = (2x^2 - 18)/(x+3) if x does not equal to -3
k if x = -3
For continuous I'm thinking k = -12 because f(-3) must equal k and the limit as x approaches -3 is -12.
I'm having trouble with differentiable though. The derivative of f(x) is 2, and if k = 2, then the derivative of that is zero, so is it not differentiable?
Thanks.