Practice question · Select all that apply
Select every statement that is TRUE of the second derivative.
Hints
- Four of these restate the lesson; one confuses a derivative with a function value.
- Ask which claim links f'' to the height of the graph rather than its bending.
Show the answer
- A. A sign change in it marks an inflection point
- B. Where it is positive the curve is concave up
- D. It measures how the slope itself is changing
- E. A negative value at a critical point signals a local maximum
Why
The second derivative is the rate of change of the slope, and its sign gives concavity, hence the classification test and the location of inflection points. It has no relationship at all to where f itself is zero, a curve can cross the axis with any curvature you like.
Practise Applications of Derivatives
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More questions on Applications of Derivatives
- Complete the definition of an inflection point.
- Each item reports how the sign of f' behaves as x passes through a critical point. Sort them.
- A point where f'(x) = 0 is always a maximum or a minimum.
- Order the steps of finding the extreme values of a function on a closed interval.
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