Vertical tangent lines? If a function f is continuous at a and , then the curve y= f(x) has a vertical tangent line at a and the equation of the tangent line is x = a. If a is an endpoint of a domain, then the appropriate one-sided derivative (Exercises 59-60) is used. Use this definition to answer the following questions. Graph the following curves and determine the location of any vertical tangent lines. a.? x2 + y2 = 9 b.? x2 + y2 + 2x = 0

SOLUTION If a function f is continuous at a and lim|f (x)| = , then the curve y= f(x) has a xa vertical tangent line at a and the equation of the tangent line is x = a STEP 1 2 2 (a). Given the function x +y = 9 2 We can write this function as y =± 9x Now,let’s differentiate this function y, 2x x Therefore y = 2 9x = 9x2 Now let us take the left hand and the right hand limits. lim|f(x)| = lim| x |= x3 x3 9x2 lim |f(x)| = lim | x 2|= x3 x3 9x Therefore,we have lim|f (x)| = lim |f(x)|...