1. Differentiation Problem

Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

find a and b such that f is differentiable everywhere

f(x)= ax^3, x=less than or equal to 2
x^2+b, x=greater than 2

thanks

2. Originally Posted by soldatik21
Can anyone help me out with this one problem please, didn't really learn this type of problem yet.

find a and b such that f is differentiable everywhere

f(x)= ax^3, x=less than or equal to 2
x^2+b, x=greater than 2

thanks
Hint: If $\displaystyle f(x)$ is differentiable everywhere, then it is continuous and smooth at all points.

Here, the only possible point of discontinuity is at $\displaystyle x = 2$.

So you need to find an $\displaystyle a$ and $\displaystyle b$ so that the function is the same at that point.

Have a go.

3. i understand that part that at x=2 the two functions have to be equal. but doesn't that give you more than one answer for example a can be 2 and can be 12? or a can be 1 and b can be 4?