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).
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!!!
Make hours to seconds to match meters 19.6*3600=70560 seconds And is dropped from a height of 15.4 meters then the velocity will be 15.4m/70560s = 0.0002182539m/s
