Schaum's Outline of Theory and Problems of Beginning Calculus

CHAP. 113 THE SLOPE OF A TANGENT LINE 9111.7 Find the point(s) on the graph of y = x2 at which the tangent line is parallel to the line y = 6x - 1. [Hint:Use Theorem 4.1.)11.8 Find the point(s) on the graph of y = x3 at which the tangent line is perpendicular to the line 3x + 9y = 4.[Hint: Use Theorem 4.2.111.9 Find the slope-intercept equation of the line normal to the graph of y = x3 at the point at which x = 4.11.10 At what point(s) does the line normal to the curve y = x2 - 3x + 5 at the point (3, 5) intersect the curve?11.11 At any point (x, y) of the straight line having the slope-intercept equation y = mx + b, show that thetangent line is the straight line itself.11.12 Find the point(s) on the graph of y = x2 at which the tangent line is a line passing through the point(2, - 12). [Hint: Find an equation of the tangent line at any point (xo, xi) and determine the value@) of xofor which the line contains the point (2, - 12).]11.13 Find the slope-intercept equation of the tangent line to the graph of y = fi at the point (4, 2). [Hint: SeeALGEBRA in Problem 10.15.1