# 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 #