Calc Question: Finding Secant Slope?

In summary, we discussed the incorrect formula \frac{-1}{(x)(x+h)} for the derivative of f(x)=\sec x and the correct formula \sec{x}\tan{x}. We also talked about the point (1,\frac{1}{2}) lying on the curve y=\frac{x}{1+x} and using a calculator to find the slope of the secant line for a given value of x (0.5). The correct slope is 1/3, which was found using the formula \frac{y_{1}-y_{2}}{x_{1}-x_{2}} and confirmed by Daniel.
  • #1
sjaguar13
49
0
I wrote down the notes from class, but when I tried to do the homework, I am not even close to the right answers. The formula I wrote down is:
[tex]\frac{-1}{(x)(x+h)}[/tex]
Apparently that's wrong. Anyone know what it's supposed to be?
 
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  • #2
Do you mean the derivative of [tex]f(x)=\sec x[/tex]? In that case it's [tex]\sec{x}\tan{x}[/tex].
 
  • #3
The point [tex]\mbox(p(1,\frac{1}{2}))[/tex] lies on the curve [tex]y=\frac{x}{1+x}[/tex].
If [tex]Q[/tex] is the point [tex](x,\frac{x}{(1+x)})[/tex], use your calculator to find the slope of the secant line [tex]PQ[/tex] for the following value of [tex]x[/tex]: 0.5

I get -2, but it's really .33333.
 
  • #4
The slope is simply
[tex] a=\frac{y_{1}-y_{2}}{x_{1}-x_{2}} [/tex]

and i get 1/3...

Daniel.
 

1. How do I find the secant slope of a function?

To find the secant slope of a function, you need to choose two points on the function and calculate the slope using the formula (change in y)/(change in x). This will give you the average rate of change between the two points.

2. Can the secant slope be negative?

Yes, the secant slope can be negative. This means that the function is decreasing between the two chosen points.

3. What is the difference between secant slope and tangent slope?

The secant slope is the average rate of change between two points on a function, while the tangent slope is the instantaneous rate of change at a single point on a function. In other words, the secant slope is the slope of a line connecting two points, while the tangent slope is the slope of the curve at a specific point.

4. How is the secant slope used in calculus?

The secant slope is used to approximate the slope of a curve at a specific point, which is important in calculating derivatives in calculus. By choosing points closer and closer together, the secant slope can give a more accurate approximation of the tangent slope.

5. Can the secant slope be used to find the equation of a tangent line?

Yes, the secant slope can be used to find the equation of a tangent line. By choosing two points closer and closer together, the secant slope will approach the tangent slope, which can then be used to find the equation of the tangent line using the point-slope formula.

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