Question

Please help with calculus!!

Find the distance between the point (5,-2) and the line which is tangent to the curve y=-x^3 + 5x^2 -2x +2 at the point (1,4)

Answer 1

First find the eqn of the tangent to the curve at (1,4).

This means differentiate the curve, find the gradient at x = 1, use the point gradient formula y - y1 = m(x - x1) to find the eqn of that tangent line.
then use the perpendicular distance formula from (5,-2) to that line.