Help with secant question , thanks

In summary: It's the function that takes x2 and returns the slope of the secant line from (x1,f(x1)) to (x2,f(x2)).
  • #1
Zephyr91
4
0
here is my question, *thanks for helping* i need it badly

Consider the curve y = f(x) where f(x) = (x-5)(2X+3)

A) Show that P1 = (x1,y1) = (0,-15) is on the curve and find and expression for the slope of the secant joining P1 with any other point P2 = (x2,f(x2)) , x2 cannot be 0 on the curve

b) Show that there is always a point x*, lying between x1 = 0 and x2 such that the slope of the tangent line to the curve at x* is equal to the slope of the secant joining P1 and P2



ok and i am stuck on a) how would i go about solving it, would i take the derivate of the curve then sub the points from P1 to find P2?
 
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  • #2
The secant line is just the line joining (x1,f(x1)) and (x2,f(x2)). There is no derivative involved - just a plain old slope.
 
  • #3
For A) what is the value of f(x) when you plug in x=0? Edit: OK, a little too late posting
 
  • #4
okay so plan old slope i would find it by doing:

m = x2 -x1 / f(x2) - f(x1)

or

slope of secant = f(0+h) - f(0) / h

m = [(o+h)-5][2(0+h)+3] - (-5)(3) / h
m = (h-5)(2h+3) + 15 / h
m = 2h^2 + 3h + 10h -15 +15 / h
m= 2h-7
?
 
Last edited:
  • #5
The first, except it's upside down. It's deltay/deltax.
 
  • #6
do i have enough info to complete the first, i don't really know how to go about doing it...
 
  • #7
Zephyr91 said:
do i have enough info to complete the first, i don't really know how to go about doing it...

I don't know what you don't know. Are you worried that you don't know x2?
 
  • #8
yeah i donty know x2
 
  • #9
Just do it anyway. What's f(x2)? Use the definition of f.
 

1. What is a secant line?

A secant line is a line that intersects a curve at two or more points.

2. How do I find the slope of a secant line?

To find the slope of a secant line, you need to choose two points on the curve and calculate the change in the y-values divided by the change in the x-values.

3. Can you explain the secant method in calculus?

The secant method is a numerical method used to approximate the roots of a function. It involves drawing a secant line between two points on the curve and using the x-intercept of the secant line as an approximation for the root.

4. How is a secant line different from a tangent line?

A secant line intersects the curve at two or more points, while a tangent line only intersects the curve at one point. Additionally, the slope of a secant line changes as the two points on the curve are moved closer together, while the slope of a tangent line remains constant.

5. Can you provide an example of using the secant method to find a root?

Sure, let's say we want to find the root of the function f(x) = x^2 - 4. We choose two points on the curve, (1,f(1)) and (3,f(3)), and use the secant method to find the x-intercept of the secant line. This gives us the approximation x = 2, which is the root of the function.

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