How do you find the slope of the secant lines of f(x) = x^2 + 5x at (6 , f(6)) and (6 + h , f(6 + h))?
1 Answer
Jan 23, 2017
Slope
Explanation:
We have
When
f(x) = 6^2+5*6
\ \ \ \ \ \ \ = 36 + 30
\ \ \ \ \ \ \ = 66
When
f(x) = (6+h)^2+5(6+h)
\ \ \ \ \ \ \ = 36 + 12h+h^2+30+5h
\ \ \ \ \ \ \ = h^2+17h+66
So the slope of the secant line at
(Delta y)/(Delta x) = (f(6+h)-f(6))/((6+h)-6)
\ \ \ \ \ \ \ = (h^2+17h+66 -66) / (h)
\ \ \ \ \ \ \ = (h^2+17h) / (h)
\ \ \ \ \ \ \ = h+17
Side Note - What is the significance of this:
If we let
With our knowledge of Calculus we can confirm this as:
f'(x)=2x+5 => f'(6)=12+5 = 17