Answer:
- x < -3/4, f'(x) = -4
- the derivative is -4 for x < -3/4; it is undefined at x = -3/4
- the derivative is +4 for x > -3/4; it is undefined at x = 3/4
- N; not differentiable. The left and right derivatives are different.
- F; not differentiable at x = -3/4.
- T; the interval does not include x = -3/4.
- F; not differentiable at x = -3/4.
- T; the interval does not include x = -3/4.
Step-by-step 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.
