# Calculus

posted by .

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 -

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 -

Thank you very much!

## Similar Questions

1. ### pre-calculus

In the following exercise, find the smallest interval for theta [from this point on i will denote theta as '*' for ease of typing] starting with * min= 0 so that your graphing utility graphs the given polar equation exactly once without …
2. ### calculus

You are given the following function. f(x)= (8+x)/(1-8x) (a) Find the derivative of the function using the definition of derivative. (b) Give the domain of the function. c) Give the domain of derivative of function?
3. ### calculus

Consider the function f(x) = piecewise [(x^3)(cos(1/x)) , x=/=0], [0, x=0]. Use the definition of the derivative at a point to determine if f is differentiable at x=0 I am not sure how to start this question. Am I supposed to plug …
4. ### calculus

Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)
5. ### Calculus

Assuming that f and g are functions differentiable at a (though we do not know their formulas). Prove that f +g is differentiable at a using the definition of the derivative.
6. ### Calculus c

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
7. ### Calculus

Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis at …
8. ### Calculus

Given f'(x)=9/2x(3x^2+2)^1/2 (this is the derivative of y= sqrt[(3x^2+2)^3]) , state any values of x for which the function is not differentiable
9. ### pre-calculus 11

I have the question what is the equation of the function in the form f(x) = 1/x-c for the function with a vertical asymptote at x=1?
10. ### Calculus

Consider the function f(x) = {0, x = 0 and 1 - x, 0 <= x <= 1}. Which of the following statements is false?

More Similar Questions