Calculus-slope of a secant line Question?

Question

For f(x)=5x(squared)+6-x: find the slope of secant line joining (2,f(2)) and (3,f(3))
show your work

Answer 1

f(x) = 5x² + 6 - x

Let (x₁, y₁) = (2, f(2)), (x₂, y₂) = (3, f(3))

Here x₁=2, y₁=f(2), x₂=3, and y₂=f(3)

Find f(2) = 5(2)² + 6 - 2 = 5(4)+4 = 20+4=24=y₁

Find f(3) = 5(3)² + 6 - 3 = 5(9)+3 = 45+3=48=y₂

The slope m of the line through thepoints (x₁, y₁) and (x₂, y₂) is given by m = (y₂-y₁) / (x₂-x₁)

m = (48-24)/(3-2) = 24

The slope m = 24.