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.

Question

f(x) = x^4sin(2/x),

if x is not equal to 0,
and
f(x) = 0

if x = 0.
If it is differentiable, what is the derivative? (If it isn't, enter dne.)
f'(0) = ________

Answer 1

I graphed it, it did what I expected. You graph it near zero.

f'=4x^3 sin(2/x)-x^4 cos(2/x)*2/x^2

f'(0)=0 YOu need to know cos(2/x) is a max of 1, a min of -1, either way, that times 0 is zero.

Answer 2

Thank you very much!