Answer the following questions related to the derivative and the tangent to a curve.
MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives
Problem
Answer the following questions related to the derivative and the tangent to a curve.
(i) Define the derivative of a function f at a point a by using the limit of the difference quotient.
(ii) Describe the geometrical meaning of the derivative at a point on the graph of f.
(iii) Explain why the existence of a finite derivative at a point guarantees a unique tangent line there.
(iv) State the point–slope form of the equation of a straight line with slope m passing through the point (x0,y0).