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Curve sketching - Calculus: (x - 2) / (x^2 - 1)
- Thread starter Tinker
- Start date
Re: Curve sketching - Calculus
If the power of the numerator is less than the power of the denominator, then the x-axis is the HA.
Graph it and you will see.
To check for inflection pts, find the 2nd derivative, set to 0 and solve for x.
The second derivative is \(\displaystyle \frac{2(x^{3}-6x^{2}+3x-2)}{(x^{2}-1)^{3}}\)
Set the numerator = 0 and solve for x. There will be 1 real solution.
For the critical points, use the first derivative.
If the power of the numerator is less than the power of the denominator, then the x-axis is the HA.
Graph it and you will see.
To check for inflection pts, find the 2nd derivative, set to 0 and solve for x.
The second derivative is \(\displaystyle \frac{2(x^{3}-6x^{2}+3x-2)}{(x^{2}-1)^{3}}\)
Set the numerator = 0 and solve for x. There will be 1 real solution.
For the critical points, use the first derivative.
Re: Curve sketching - Calculus
Sweet . . . but the HA is crossed when graphed?? And with the f"(x), I set f" to 0 =(x^3-6x^2+3x-2) . . . how does one solve for x? Thanks for your response and one other question if I may . . . how do you post in the nifty little functions (without having to use the ^ for exp)?
Sweet . . . but the HA is crossed when graphed?? And with the f"(x), I set f" to 0 =(x^3-6x^2+3x-2) . . . how does one solve for x? Thanks for your response and one other question if I may . . . how do you post in the nifty little functions (without having to use the ^ for exp)?
D
Deleted member 4993
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Re: Curve sketching - Calculus
Tinker said:Sweet . . . but the HA is crossed when graphed?? Yes that can happen - only once.
And with the f"(x), I set f" to 0 =(x^3-6x^2+3x-2) . . . how does one solve for x? Best way to estimate the root is to graph it. There are other numerical schemes - through which it can be shown that the root of the given cubic function is at x = 5.522333393
Thanks for your response and one other question if I may . . . how do you post in the nifty little functions (without having to use the ^ for exp)?