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.
a. Find f′(x).
b. Calculate the coordinates of P and of Q.
c. Write down the coordinates of the point where the tangent at P intersects N2.
d. Write down the coordinates of the point where the tangent at Q intersects N1.