Consider the curve f(x) = 3/(x − 3). Find the slope of the line connecting the points. Sketch the curve and those secant lines.
(a) (5, f(5)) and (5.2, f(5.2))

(b) (5, f(5)) and (4.8, f(4.8))

Find the slope of the line through (5, f(5)) and (5+ h, f(5 + h)). Simplify the expression

Consider what happens to that expression as h gets closer and closer to 0

What is the slope of the tangent line to the curve at x = 5?

Write an equation of the tangent line to the curve at
x = 5.
(Let x be the independent variable and y be the dependent variable.)

Question

Consider the curve f(x) = 3/(x − 3). Find the slope of the line connecting the points. Sketch the curve and those secant lines.
(a)    (5, f(5)) and (5.2, f(5.2))

  
(b)    (5, f(5)) and (4.8, f(4.8))

Find the slope of the line through (5, f(5)) and (5+ h, f(5 + h)). Simplify the expression

Consider what happens to that expression as h gets closer and closer to 0

What is the slope of the tangent line to the curve at x = 5?
 
Write an equation of the tangent line to the curve at 
x = 5.
 (Let x be the independent variable and y be the dependent variable.)