Practice question · True or false
The derivative at a point is the slope of the secant line through two nearby points on the curve.
Hints
- A secant needs two distinct points.
- What happens as the second point slides in?
Show the answer
False
Why
False. That is the difference quotient, an approximation; the derivative is its limit as the two points merge, which turns the secant into the tangent. The distinction matters because the limit can fail to exist, at a corner the secants approach different slopes from each side and there is no derivative.
Practise The Derivative
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