MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
Let the quadratic function be y=x2+kx+1, where k is a real constant.
(i) Find dxdy in terms of x and k.
(ii) The tangent to the curve at the point where x=1 passes through the point (3,−5). Determine the value of k that satisfies this condition.
(iii) For the value of k obtained in part (ii), obtain the equations of (a) the tangent and (b) the normal to the curve at x=1.