Find values of the constants a and b for which the following function is continuous but not differentiable.
In other words, the graph of the function should have a sharp corner at the pont (0,f(0)).
I'm not even sure what they are asking. This is part of a limit course and I am very familiar with limits.
You will need to know at least something about derivatives to solve this problem (otherwise how can you be sure that it's not differentiable). The derivative of at 0 is 2, and the derivative of ax+b is a, so since they want it to be not differentiable, .
For it to be continuous, the limit from the right (using ax+b) must be equal to the limit from the left (using ). You should be able to calculate those two limits and set them equal to get an equation for b.
P.S. earboth beat me to the answer.
I understand derivatives, I should probably have mentioned that.
However I don't understand why the derivative of sin2x at 0 is 2. The derivative of sinx is cosx so I assume the derivative of sin2x is cos2x...The derivative of sin(2*0) is 0 and the derivative of cos(2*0) is 1...How do you get 2?
EDIT: Something tells me I am supposed to be using chain/product rule. If so then I have to vent some frustration at these courses all over the net. They ask you to solve problems which you have not learned every single time when teaching derivatives.
EDIT2: Solved with chain rule. Jesus Christ, I like how these morons shoe-horn chain rule in the problems before properly teaching derivatives! Thanks sent to you both!