Post a New Question

secant line, tangent line

posted by .

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.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. alison

    I have to do a lot of homework problems like this but I do not really understand how to do any of them. Can someone show me how to do this one so I can do the rest of my homework problems on my own?
  2. alison

    I have to do a lot of homework problems like this but I do not really understand how to do any of them. Can someone show me how to do this one so I can do the rest of my homework problems on my own?
  3. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant …
  4. Calculus

    Find an equation of the line that is tangent to the graph of f and parallel to the given line. Funtion: f(x)=1/sqrt(x-1) Line: x+2y+7=0
  5. calculus

    a. find an equation for the secant line through the points where x has the given values. b. find a equation for the line tangent to the curve when x has the first value. y=9square root(x); x=16, x=25
  6. Calculus

    1. On what interval is the function f(x)=x^3-4x^2+5x concave upward?
  7. Calculus

    Graph the function f(x)=x+4/x Graph the secant line that passes through the points (1,5) and (8,8.5) on the same set of axes Find the number c that satisfies the conclusion of the Mean Value Theorem for f on [1,8] c= Notice that if …
  8. Math

    Consider the graph of the parabola ​f(x)equals=x squaredx2. For xgreater than>0 and hgreater than>​0, the secant line through​ (x,f(x)) and ​(xplus+​h,f(x+h)) always has a greater slope than the …
  9. Math (Secant Lines)

    Consider the function f(x)=sqrt(x) and the point P(4,2) on the graph of f?
  10. Math (Calculus) (mean value theorem emergency)

    Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c in …

More Similar Questions

Post a New Question