Practice question · Select all that apply
Select every TRUE statement about the derivative.
Hints
- One implication between continuity and differentiability holds and the reverse does not.
- Use the absolute value of x at 0 to test two of the options at once.
Show the answer
- A. A sharp corner blocks differentiability
- D. Every differentiable function is continuous
- E. How steeply the curve rises at x is exactly what f'(x) reports
Why
Differentiability implies continuity but not conversely, the absolute value is the standard witness, and its corner is exactly the obstruction. And f'(x) = 0 says the graph is momentarily FLAT at x, saying nothing whatever about its height.
Practise The Derivative
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