MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Consider the function g(x)=x2.
(i) Write the difference quotient hg(x+h)−g(x).
(ii) Simplify the expression obtained in part (i) and evaluate the limit as h→0 to find g′(x).
(iii) Hence determine the slope of the tangent to the curve y=x2 at the point (1,1).