(i) Define the derivative of a function at a point using the limiting process. (ii)…
MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
(i) Define the derivative of a function at a point using the limiting process.
(ii) Suppose a curve is given by y=f(x) and f is differentiable at x=a. Starting from the definition in part (i), derive the general equation of the tangent to the curve at the point (a,f(a)).
(iii) Use your result from part (ii) to obtain the equation of the tangent to the curve y=x2 at the point where x=2.