Find the slope of the secant line problem

[killasnake]

Hi can you guys help me with this question. It asks you to find the slope of the secant line but I have no idea how to solve for it.

The point P(4,28) lies on the curve y=x^2+x+8. If Q is the point (x,x^2+x+8), find the slope of the secant line PQ for the following value of x.

if x=4.1, the slope of PQ is ________

and if x=4.01, the slope of PQ is ________

and if x=3.9, the slope of PQ is ________

and if x=3.99, the slope of PQ is ________

Based on the above results, guess the slope of the tangent line to the curve at P(4,28)__________

 

[wjm11]

The point P(4,28) lies on the curve y=x^2+x+8. If Q is the point (x,x^2+x+8), find the slope of the secant line PQ for the following value of x.

if x=4.1, the slope of PQ is ________

and if x=4.01, the slope of PQ is ________

and if x=3.9, the slope of PQ is ________

and if x=3.99, the slope of PQ is ________

Hello Killasnake,

Just plug in the given x value and find the corresponding y value.
You now have another point on the curve, pt Q.
Calculate the slope between the two points, P and Q.
Do this for all four bvalues of x, as specified.
The x values you are using are a little bit above and below x = 4, so the slopes you calculate should be a little above and below the slope of the tangent at x = 4.

 

[killasnake]

I found all of the slopes

9.1
9.01
8.9
8.99

But when it asks you

Based on the above results, guess the slope of the tangent line to the curve at P(4,28)_______

what do I do here?

 

[wjm11]

The slop at 4 is in between the slopes you've calculated. the slope is 9.

 

[killasnake]

oh... sorry didn't understand the question :?