For the function g(x) = 3x + 2 Express the slope of the secant line in terms of

ID: 3114204 • Letter: F

Question

For the function g(x) = 3x + 2 Express the slope of the secant line in terms of x and h. Find msec for h= 0.5, 0.1, and 0.01 atx= 1, what value does msec approach as h approaches 0? Find the equation for the secant line at 1 with h =0.01 Graph g and the secant line found in part (c) on the same viewing window. (b) For h = 0.5 at x= 1, what is the value of msec? (Round to two decimal places as needed.) mear For h #0.1 at x= 1, what is the value of msec? msec = (Round to two decimal places as needed.) For h #0.01 at x = 1, what is the value of msec? msec = Round to two decimal places as needed.) What value does msec approach as h mea | (Type an integer or a decimal.) (c) Find the equation for the secant line at x= 1 with h =0.01 approaches 0? Type the expression in slope-intercept form. Round coefficients to two decimal places as needed.) (d) Which of the following is the graph of g and the secant line? A. Click to select your answer(s).

Explanation / Answer

SOLUTION:

(a) We are given a function g(x)=3x+2

Now slope of secant function in terms of x and h

It is given as [f(x+h)-f(x)]/h

[3(x+h)+2-(3x+2)]/h =[3x+3h+2-3x-2]/h= (3h)/h =3

(b) we have to find the Msec

(i) for h=0.5 and x=1, we have f(x+h)=3(x+h)+2=3(1+0.5)+2=6.5 and f(x)=3x+2=3*1+2=5,

SO, [f(x+h)-f(x)]/h=(6.5-5)/0.5=3

(ii) for h=0.1 and x=1, we have f(x+h)=3(x+h)+2=3(1+0.1)+2=5.3 and f(x)=3x+2=3*1.1+2=5,

SO, [f(x+h)-f(x)]/h=(5.3-5)/0.1=3

(iii) for h=0.01 and x=1, we have f(x+h)=3(x+h)+2=3(1+0.01)+2=5.03 and f(x)=3x+2=3*1+2=5,

SO, [f(x+h)-f(x)]/h=(5.03-5)/0.01=3

for x=1 , we have y=g(1)=3*1+2=5 and the slope msec is 3 for x=1 and h=0.01 (calculated above)

SO from here we can calculate b as 5=3*1+b or b= 5-3=2

So equation = y= 3x+2

(d) clearly we can see that only option B clearly shows the appropriate graph. for g and the secant line.

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For the function g(x) = 3x + 2 Express the slope of the secant line in terms of

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