- #1
peterk
- 2
- 0
Here is a piecewise polynomial function:
f(x) = x^2 + 1 if x <= 1
f(x) = 2x if x > 1
I need to prove that this function is differentiable at x = 1?
It's a parabola that turns into a line. It doesn't have any gaps or corners. The limit of f(x) as x approaches 1 is 2, and the limit of f'(x) as x approaches 1 is 2.
This was a problem on a test, but my calculus teacher took points off because she says that the function is not differentiable at x = 1.
Thanks in advance!
f(x) = x^2 + 1 if x <= 1
f(x) = 2x if x > 1
I need to prove that this function is differentiable at x = 1?
It's a parabola that turns into a line. It doesn't have any gaps or corners. The limit of f(x) as x approaches 1 is 2, and the limit of f'(x) as x approaches 1 is 2.
This was a problem on a test, but my calculus teacher took points off because she says that the function is not differentiable at x = 1.
Thanks in advance!