Differentiability

Grade 12 Maths — Differentiability: 25 practice questions with instant scoring and explanations.

1. A function f is differentiable at x = a if:
2. If a function is differentiable at x = a, then it is:
3. The function f(x) = |x| at x = 0 is:
4. A function has a corner at x = a if:
5. The derivative f'(a) from the right is:
6. For differentiability at x = a, the left and right derivatives must:
7. The function f(x) = x^(1/3) at x = 0:
8. If f is differentiable on (a, b), then f is:
9. The derivative represents:
10. A function has a cusp at x = a if:
11. For a function to be differentiable at x = a, it must first be:
12. The second derivative f''(a) is:
13. If f'(a) = 0 and f''(a) > 0, then x = a is a:
14. A function has a vertical tangent at x = a if:
15. All polynomial functions are differentiable:
16. The function f(x) = sin(x) is differentiable:
17. If f is differentiable at x = a, then f'(a) is equal to:
18. Differentiability is a _______ condition than continuity.
19. For the function f(x) = √|x| at x = 0:
20. If a function is differentiable at every point in its domain, it is called:
21. The existence of f'(a) implies:
22. A function with a jump discontinuity at x = a is:
23. The absolute value function |x| is differentiable on:
24. Question?
25. Question?