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1.2 Derivatives Basic Concepts – Tangent and Derivatives

Chord, Secant, and Tangent

  • A chord is a line segment joining two points on a curve, like the line AB in the previous example.
  • A secant is a line that passes through two points, which means that it can be longer than a chord for any given two points A and B.
Picture 1
  • Graphically, ‘a tangent though a curve at point P’ is defined as a line that passes through P and its gradient equals the curve’s instantaneous rate of change at P.
  • Suppose P has coordinates P(p,\:f(p)), then \text {Gradient of tangent at } P=\lim _{h \rightarrow 0} \frac{f(p+h)-f(p)}{h}

Note: Here, h \rightarrow 0 is used and not h \rightarrow 0^{+}.

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