Determine if the function defined below is differentiable at

Determine if the function/ defined below is differentiable at 1. If it is, calculate f\'(1). F(x) = {2x + 5 if x =1.

Solution

For a function to be differentiable, it has to be continuous. This function f(x) f(1-) = 7 f(1+) = 7 More generally, if x0 is a point in the domain of a function ƒ, then ƒ is said to be differentiable at x0 if the derivative ƒ\'(x0) is defined. This means that the graph of ƒ has a non-vertical tangent line at the point (x0, ƒ(x0)), and therefore cannot have a break, bend, or cusp at this point. So, f\'(1-) = 1 and f\'(1+) = 18 since they are not equal, so the function is not differentiable at 1