What is the average gradient between two points on a curve?
AThe gradient of the curve at each one
BThe distance between the two points
CThe gradient of the line through them
DThe average of the two input values
Answer & Solution
Correct answer: C. The gradient of the line through them
1. The gradient of a curve is different at every point on it.
2. The average gradient between two points is the gradient of the straight line through them.
3. That straight line is worked out from the vertical change over the horizontal change.
4. It is an average, so it does not give the steepness at any one single point.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 5: Functions_
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