Let . The tangents to the curve of at the points and are parallel to the -axis, where…
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Let f(x)=x3−3x2−24x+1.
The tangents to the curve of f at the points P and Q are parallel to the x-axis, where P is to the left of Q.
Let N1 and N2 be the normals to the curve at P and Q respectively.
(1) Find f′(x).
(2) Calculate the coordinates of P and of Q.
(3) Write down the coordinates of the point where the tangent at P intersects N2.
(4) Write down the coordinates of the point where the tangent at Q intersects N1.