f(x) = squareroot 8- 68 Note that the slope of the secant line connecting any po

Question

f(x) = squareroot 8- 68 Note that the slope of the secant line connecting any point on the curve of f(x) and the point (9, 2) is secant slope = squareroot 8(9 + h) - 68 -2/h where h is the difference between x_0 = 9 and x = 9 + h. For the given points that are shown in the graph, determine h and the slope of the secant line connecting (9, 2) with (9 + h, f (9 + h)). x = 8.5 h = slope of secant line = X = 9.5 h = slope of secant line = X = 8.75 h = slope of secant line = X = 9.25 h = slope of secant line =

Explanation / Answer

we have given function f(x)=sqrt(8x-68), secant slope is [sqrt(8*(9+h)-68)-2]/h and x0=9 and x=9+h

for x=8.5 ,h=8.5-9=-0.5 since h is the difference between x0=9 and 8.5=9+h

secant slope =[sqrt(8*(9-0.5)-68)-2]/(-0.5)=4

for x=9.5 ,h=9.5-9=0.5 since h is the difference between x0=9 and 9.5=9+h

secant slope = [sqrt(8*(9+0.5)-68)-2]/(0.5)=1.656

for x=8.75,h=8.75-9=-0.25 since h is x-9

secant slope=[sqrt(8*(9-0.25)-68)-2]/(-0.25) =2.343

for x=9.25,h=9.25-9=0.25 since h=x-9

secant slope=[sqrt(8*(9+0.25)-68)-2]/(0.25)=1.797

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