Posted by **Jen** on Saturday, October 28, 2006 at 10:59pm.

f(x) = sqrt(x-1), 1<=x<=3

Let A = (a,f(a)), and B = (b,f(b)).

Write an equation for

1. the secant line AB

2. a tangent line to f in the interval (a,b) that is parallel to AB

Thank you for all the help.

For the line, you have two points,

y=mx+b put the two points in, and solve for the two unknowns, m, and b. Two equations, two unknowns.

For 2) Take the derivative, set it equal to the slope m in the above solution, solve for x, then, knowing f(x), solve for y (f(x)).

I will be happy to critique your work.

Thanks. I did this for f(x) = x + 1/x. 0.5<=x<=2

I got the points as A(.5,2.5) and B(2,2.5)

Plugged it in y=mx+b, and got

m=0 & b=2.5

So the eq. is y = 2.5

For 2, I took derivative and solved for x. I got x = +1, -1

So y = 1+1/1 = 2

Do we ignore -1?

Ignore it. The original function was

f(x) = sqrt(x-1), 1<=x<=3 , so x=-1 is outside the domain.

## Answer this Question

## Related Questions

- calculus - 5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the ...
- Calculus - Graph the function f(x)=x+4/x Graph the secant line that passes ...
- alison - I have to do a lot of homework problems like this but I do not really ...
- alison - I have to do a lot of homework problems like this but I do not really ...
- calculus - a. find an equation for the secant line through the points where x ...
- calculus - i'm not sure how to do this. can someone help, please? thanks! ...
- pre calc - f(x)=-3x+2 a) express the slope of the secant line of each function ...
- College Calculus - Let f(x) = 3x^2 - 2x + 1 a) write an equation of the line ...
- cal - find the equation of a quadratic function whose graph is tangent at x=1 to...
- calculus - find the equation of a quadratic function whose graph is tangent at x...