l 31 How is the difference quotient related to slope tangent

l 31. How is the difference quotient related to slope? tangent line to a curve at 32. to Figure 93. How is the secant line PQ related to the point For each of the functions in Erercises 33-40, find (a) f(x h). (b) f(x h) f(a f(x h) f(x) See Example 4. and (c) 35, f(x) 6x 2 34, f(x) 1 x 33, f(r) 2 x 36. for 4x 11 37. f(x) -2 5 38. f(x) 4x 2 39. f(x) 40. f(x) 41. f(x) 42. f(x) -x 45. f(r) x2 3x 1 46, f(x) 4x 2 Let f(r)

Solution

(39) f(x) = 1/x

(a) f(x+h) = 1/(x+h)

(b) f(x+h) - f(x)

= 1/(x+h) - 1/x

(c) [f(x+h) - f(x)] / h

=  {1/(x+h) - 1/x }/h

= 1/x(x+h)

Answer