Tangent lines problems and their solutions, using first derivatives, are presented.
Problem 1Find all points on the graph of y = x^{ 3} - 3 x where the tangent line is parallel to the x axis (or horizontal tangent line).Solution to Problem 1:
Problem 2Find a and b so that the line y = - 3 x + 4 is tangent to the graph of y = a x^{3} + b x at x = 1.Solution to Problem 2:
Problem 3Find conditions on a and b so that the graph of y = a e^{ x} + bx has NO tangent line parallel to the x axis (horizontal tangent).Solution to Problem 3:
Exercises1) Find all points on the graph of y = x^{ 3} - 3 x where the tangent line is parallel to the line whose equation is given by y = 9 x + 4. 2) Find a and b so that the line y = - 2 is tangent to the graph of y = a x^{2} + b x at x = 1. 3) Find conditions on a, b and c so that the graph of y = a x^{ 3} + b x^{ 2} + c x has ONE tangent line parallel to the x axis (horizontal tangent). Solutions to the Above Exercises1) (2 , 2) and (-2 , -2) 2) a = 2 and b = - 4 3) 4 b^{ 2} - 12 a c = 0 More references on calculus problems |