Question

Consider the function f(x) = √x and the point P(4,2) on the graph f.

a)Graph f and the secant lines passing through the point P(4, 2) and Q(x, f(x)) for x-values of 3, 5, and 8.

b) Find the slope of each secant line. (Round your answers to three decimal places.)
(line passing through Q(3, f(x)))
(line passing through Q(5, f(x)))
(line passing through Q(8, f(x)))

c)Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(4,2).

d) Describe how to improve your approximation of the slope. (multiple choice)

-Choose secant lines that are nearly horizontal.

-Define the secant lines with points closer to P.   

-Define the secant lines with points farther away from P

-Choose secant lines that are nearly vertical.

Answer 1