Practice question · Select all that apply
A function f satisfies f(4) = 100 and f'(4) = -2. Select every statement that follows.
Hints
- Separate what the sign of f' tells you from what the size of f' tells you, and keep both apart from f itself.
- A large value can be shrinking slowly.
Show the answer
- C. The function is changing slowly compared with a point where the derivative is -50
- D. The function is decreasing at x = 4
- E. The tangent line at x = 4 slopes downward
Why
A negative derivative means falling, and its small size means falling gently. Nothing about f' constrains the height: f(4) is 100, firmly positive, and at 2 units of fall per unit of x it would take about 50 units of x to reach zero.
Practise Derivatives and Rates of Change
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