f(x)=40+4x+x^2 (e) What is the slope of the chord connecting the points (5, f (5)) and (5 + ∆x, f (5 + ∆x)), when ∆x = 5? Really confused on how to do this and what it means

19

Step-by-step explanation:

So we have the function:

And we want to find the slope of the chord that connects the points (5,f(5)) and (5+Δx, f(5+Δx)).

So first, find the two points.

1) (5,f(5))

Substitute in 5 for x:

Square and multiply:

Add:

So, our first point is (5,85)

2) (5+Δx, f(5+Δx))

Remove the Δx by substituting it with 5. Thus:

Now, substitute in 10 for x. Thus:

Square and multiply:

Add:

So our second point is (10,180).

Now, just find the slope between (5,85) and (10,180) using the slope formula:

Let (5,85) be x₁ and y₁ and let (10,180) be x₂ and y₂. Substitute:

Subtract:

Divide:

So, the slope that connects the chord is 19.

And we are done :)

351.23

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x