The tangent line to a curve is the one that coincides with the curve at a point and with the same derivative, that is, the same degree of variation. We have then: y = 5x-x² Deriving: y '= 5-2x In point (1, 4) The slope is: y (1) '= 5-2 * (1) y (1) '= 3 The equation of the line will be: y-f (a) = f '(a) (x-a) We have then: y-4 = 3 (x-1) Rewriting: y = 3x-3 + 4 y = 3x + 1 Answer: the tangent line to the parabola at the point (1, 4) is y = 3x + 1 the slope m is m = 3
