Question

Help solving this derivative function?

Answer 1

1. x < -3/4, f'(x) = -4
2. the derivative is -4 for x < -3/4; it is undefined at x = -3/4
3. the derivative is +4 for x > -3/4; it is undefined at x = 3/4
4. N; not differentiable. The left and right derivatives are different.
5. F; not differentiable at x = -3/4.
6. T; the interval does not include x = -3/4.
7. F; not differentiable at x = -3/4.
8. T; the interval does not include x = -3/4.

Explanation:

As indicated in the attached graph, the derivative is discontinuous and undefined at x = -3/4.

Ordinarily, questions such as the 2nd and 3rd ones would use a notation such as -3/4⁻ or -3/4⁺ to indicate the derivative near, but not at, the point of interest on the left- or right-sides, respectively. Coming at the point from the left or right doesn't matter—the derivative at x=-3/4 is undefined either way.