Posted by **Abigail** on Wednesday, February 23, 2011 at 7:29pm.

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^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) = ________

- Calculus -
**bobpursley**, Wednesday, February 23, 2011 at 7:37pm
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.

- Calculus -
**Abigail**, Wednesday, February 23, 2011 at 7:42pm
Thank you very much!

## Answer this Question

## Related Questions

- Calculus - Assuming that f and g are functions differentiable at a (though we do...
- calculus - Consider the function f(x) = piecewise [(x^3)(cos(1/x)) , x=/=0], [0...
- Calculus c - Let f be a twice-differentiable function defined on the interval -1...
- Calculus - Let f be a twice-differentiable function defined on the interval -1.2...
- calculus - You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the...
- calculus - Find the derivative of the function using the definition of ...
- pre-calculus - In the following exercise, find the smallest interval for theta [...
- Calculus - Use the graph of f(x)=x^2/(x^2-4) to determine on which of the ...
- Calculus (Continuity) - If the following function is continuous, what is the ...
- Calculus (Continuity) - If the following function is continuous, what is the ...