Question

Calculus homework, please help!

Answer 1

what does it mean to differentiable at a point?

Answer 2

In a nutshell, it means that the limit as h->0 of the difference quotient exists for that value of x.

Answer 3

in this context, if f is to be differentiable at x = 2 it means that
\[\frac{ d(2x^2+4) }{ dx }=\frac{ d(mx+b) }{ dx } \text{ and } 2(2)^2+4 = m(2)+b\]

Answer 4

@DebbieG got most of it... the function must also be contiuous at that point

Answer 5

Right... in this case, f(2) exists, so if the limit of the DQ exists that will pretty much take care of continuity. :)

Like @pgpilot326 said, what you really want is to find mx+b so that the point on THAT line, at x=2, is =f(2).

Answer 6

no it won't take care of continuity. it will only take of the slope. f is not necessarily continuous at 2 but continuity is a necessary condition for the derivative to exist.

Answer 7

@pgpilot326 @DebbieG I need to find m