Answer:
a) slope of secant line = 3
b) slope of tangent line = 2
Step-by-step explanation:
Given:
- The function:
f(x) = x^2 -2*x - 3
- The slope for f(x) @ x = 2 is:
slope = h + 2
Find:
a) The slope of the secant line through (2, f(2)) and (3, f(3))
b) The slope of the tangent line at x = 2
Solution:
- Since we are given the slope of the line computed via secant method. All we need to do is evaluate the slope given for respective question.
- The slope of secant line between points ( 2 , f(2) ) and ( 3 , f(3) ) is:
slope = h + 2
Where, h is the step size between two points. h = 3 - 2 = 1
slope = 1 + 2 = 3
Hence, the slope of the secant is 3.
- The slope of tangent line @ points ( 2 , f(2) ) is:
slope = Lim _ h-->0 (h + 2)
Where, h step size is reduced to infinitesimal small number. Hence, h = 0
slope = 0 + 2 = 2
Hence, the slope of the tangent is 2.
