Question

The point P(7, −4) lies on the curve y = 4/(6 − x). (a) If Q is the point (x, 4/(6 − x)), use your calculator to find the slope mPQ of the secant line PQ (correct to six decimal places) for the following values of x. (i) 6.9 mPQ = (ii) 6.99 mPQ = (iii) 6.999 mPQ = (iv) 6.9999 mPQ = (v) 7.1 mPQ = (vi) 7.01 mPQ = (vii) 7.001 mPQ = (viii) 7.0001 mPQ = (b) Using the results of part (a), guess the value of the slope m of the tangent line to the curve at P(7, −4). m = (c) Using the slope from part (b), find an equation of the tangent line to the curve at P(7, −4).

Answer 1

Hopefully you have a Ti-84 calculator because that's what I'm going to use.

First, input the equation on the "y =" button and graph the equation.

Then, hit "2nd, trace", or "calc". Choose the 6th option, "dy/dx". This gives you the derivative, or slope of the secant line, at any given x value.

If you just start typing numbers and hit enter, it'll find the derivative, so for part a letters i-viii, just input those numbers and press enter.

From the looks of it, the slope approaches 4 (as you from the x-values in i-iv and v-viii, the slopes approach 4). You can also check this by just inputting the x-value 7 in dy/dx or taking the derivative of the equation and plugging in 7. Hope this helps!! If you liked this answer please rate it as brainliest!!!