Question

Find the slope of the secant line between the values and for the function given below:

f(x) = √(x+6); x₁ = c, x₂ = c+h; c > -6
The slope of the function is _________?

Answer 1

The slope of the secant line for the function f(x) = √(x+6) between x₁ = c and x₂ = c+h, with c > -6, is found using the formula m = (√(c+h+6) - √(c+6)) / h.

Step-by-step explanation:

To find the slope of the secant line for the function f(x) = √(x+6) between x₁ = c and x₂ = c+h, where c > -6, we'll apply the definition of the slope of a secant line. The slope is the change in f(x) over the change in x, which can be calculated using the formula:

m = (f(c+h) - f(c)) / ((c+h) - c)

Substituting the given values, we have:

m = (√(c+h+6) - √(c+6)) / h

This formula will give the slope of the secant line between x₁ and x₂ for the given function.