The point P(2,1) lies on the curve y=1/(1x)
If Q is the point (x, 1/(1x) find slope of secant line.
these are the points
2, 1
1.5,2
1.9,1.111111
1.99,1.010101
1.999,001001
2.5,0.666667
2.1,0.909091
2.01,0.990099
2.001,0.999001
using the results from the points guess the value of the slope of tangent line to the curve at P(2,1)
then find equation
the slope answer was 1
would you set it up like this
(1/(12)+1)/(21) the answer comes to zero
then the equation was y=x3
how?
 👍
 👎
 👁
 ℹ️
 🚩
1 answer

Now that you have the slope and a point on the line, recall how you found the equation of a straight line , (the secant), from earlier grades
in the form y = mx + b
y = x + b , since m = 1
plug in the point (2,1)
1 = 2 + b
b = 3
so y = x  3
or
y(1) = 1(x2)
y + 1 = x  2
y = x  3
or
x  y  3 = 0 👍
 👎
 ℹ️
 🚩
Answer this Question
Related Questions

Calculus
The line that is normal to the curve x^2=2xy3y^2=0 at(1,1) intersects the curve at what other point? Please help. Thanks in advance. We have x2=2xy  3y2 = 0 Are there supposed to be 2 equal signs in this expression or is it x2 + 2xy  3y2 = 0 ? I'll

MATHPlease help!!
I'm desperate! Find the point where the curve r(t)=(12sint)i  12(cost)j+ 5tk is at a distance 13pi units along the curve from the point (0,12,0) in the direction opposite to the direction of increasing arc length. Thanks for any advice...

Calculus 1
The curve y = x/(sqrt(5 x^2)) is called a bulletnose curve. Find an equation of the tangent line to this curve at the point (2, 2)

Calculus
The curve y = x/(1 + x^2) is called a serpentine. Find an equation of the tangent line to this curve at the point(2, 0.40).(Round the slope and yintercept to two decimal places.)

calculus
Notice that the curve given by the parametric equations x=25−t^2 y=t^3−16t is symmetric about the xaxis. (If t gives us the point (x,y),then −t will give (x,−y)). At which x value is the tangent to this curve horizontal? x = ? At which t value is

AP Calculus
Consider the curve given by x^2+4y^2=7+3xy a) Show that dy/dx=(3y2x)/(8y3x) b) Show that there is a point P with xcoordinate 3 at which the line tangent to the curve at P is horizontal. Find the ycoordinate of P. c) Find the value of d^2y/dx^2 (second

calculus
The point P(4, −2)lies on the curve y = 2/(3 − x). (a) If Q is the point(x, 2/(3 − 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. 1) 3.9 mPQ= 2) 3.99 mPQ= 3)3.999

math
Um... i cant find anything about this in the textbook, help??!! 1. m  7 < 6 (1 point) m < 1 m > 1 m < 13 m < 13 2. x + 4.5 > 5.5 (1 point)  x > 10  x > 1  x > 0.1  x < 1  3. p + 12 > 9 (1 point) p > 21 p > 3 p > 21 p > 3 4. Translate the

Trig
The angular speed of a point on a planet is 3pi/7 radian per hour. The equator lies on a circle of radius approximately 9000 miles. Find the linear velocity, in miles per hour, of a point on the equator.

Calculus
Suppose the point (pi/3, pi/4) is on the curve sinx/x + siny/y = C, where C is a constant. Use the tangent line approximation to find the ycoordinate of the point on the curve with xcoordinate pi/3 + pi/180.

Ap calc.. Dying!! Please help!
Given the curve x^2xy+y^2=9 A) write a general expression for the slope of the curve. B) find the coordinates of the points on the curve where the tangents are vertical C) at the point (0,3) find the rate of change in the slope of the curve with respect

calculus
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 =

Calc AB
Suppose that f(x) is an invertible function (that is, has an inverse function), and that the slope of the tangent line to the curve y = f(x) at the point (2, –4) is –0.2. Then: (Points : 1) A) The slope of the tangent line to the curve y = f –1(x) at

Calculus 1
The curve with the equation y^2=5x^4x^2 is called a kampyle of Eudoxus. Find an equation of the tangent line to this curve at the point (1,2).

AP Calculus
Consider a curve given implicitly by the equation (1+x)y^3 + (x^4)y  85 = 0. A. Calculate dy/dx at a general point (x,y). B. Write the equation of the tangent line to the curve at the point (3,1). C. At (3,1), y(x) is defined implicitly as a function of

calculus
Find the area of the region that lies inside the first curve and outside the second curve. r = 1 + cos(θ), r = 2 − cos(θ)

Math
1. What is the value of 14 – a2 given a = –3? (1 point) 23 11 8 5 2. Which equation represents “fifteen more than r is sixtyone?” (1 point) r + 61 = 15 r + 15 = 61 r – 15 = 61 r – 61 = 15 3. What is the value of 42 – 2(3 • 5 + 1)? (1

Calc 1
The point (1,0) lies on the curve y=sin(10π/x). A) if Q is the point (x,sin(10π/x), find the slope of the secant line PQ. Points are 2,1.5,1.4,1.3,1.2,1.1,0.5,0.6,0.7,0.8,0.9 Do slopes appear to be approaching a limit? There is no 10π/x on the unit

Calculus
Find the maximum distance from the curve y=2√2x to the point (6, 0).

Calculus I
Find the point on the curve y=x^2 closest to point (0,1) Here's what I have: Sqrt {(x0)^2 + ((x^2)1)} Sqrt {((x^2) + (x^2)1} d= sqrt (x^4)1 y= (x^4)1 Fprime(x) = 4x^3 Domain = ARN Critical Number x= 0 Any help or comments would help alot. Thanks!
Still need help?
You can ask a new question or browse existing questions.