Homework SourseDecide if the following function fx is differentiable at x0
Decide if the following function f(x) is differentiable at x=0. Try zooming in on a graphing calculator, or calculating the derivative f\'(0) from the definition.
f(x)=x^2sin(5/x)
if x=0, and
f(x)=0
if x=0.
If it is differentiable, what is the derivative? (If it isn\'t, enter dne.)
f(0)=
f(x)=x^2sin(5/x)
if x=0, and
f(x)=0
if x=0.
If it is differentiable, what is the derivative? (If it isn\'t, enter dne.)
f(0)=
Solution
A function must exist at a given point in order to be differentiable at that point.
f(x) = x^2 sin(5/x)
f does not exist when x = 0, so f\' does not exist when x = 0.
