alleryStart learning →The gradient at a single point on a curve is the gradient of what?
AThe curve at every point
BThe chord across the curve
CThe axis through that point
DThe tangent at that point
Answer & Solution
Correct answer: D. The tangent at that point
1. As two points on a curve move closer together, the line through them turns.
2. When the two points overlap, that line touches the curve at one point only and is called a tangent.
3. The gradient at a point on a curve is the gradient of the tangent at that point.
4. A chord cuts the curve at two separate points, so it gives an average instead.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 5: Functions_
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