Consider the curve with equation

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Consider the curve with equation f(x)=3x2f(x) = 3x^2. The point P(a,3a2)P(a, 3a^2) lies on the curve. (1) Find the gradient to the curve at x=ax = a. (2) Show that the equation of the tangent line to the curve at point P(a,3a2)P(a, 3a^2) has equation y=6ax−3a2y = 6ax - 3a^2. (3) Given that the tangent line passes through the point A(0,−3)A(0, -3) find the possible values of aa. (4) Hence, find the equations of the tangent lines passing through A(0,−3)A(0, -3).

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