- #1
How to Solve a Cubic Equation Involving Derivatives and Substitutions?
In summary: Then ##x = \frac{c \pm \sqrt{6m}}{6}##.In summary, the conversation discusses finding critical points for a given function and solving for x in f'(x) = 0. There is some discrepancy in the values found, but it is determined that there was a typing error in the original problem. The process of solving for x is simplified by not substituting for c^2 until later.
- #2
Buzz Bloom
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Hi Ameer:
I also found two values for x for which f'=0, but my values are different than yours. Might you have copied the problem incorrectly?
Regards,
Buzz
I also found two values for x for which f'=0, but my values are different than yours. Might you have copied the problem incorrectly?
Regards,
Buzz
- #3
Mark44
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Since the problem is shown as an image, I don't see how it could have been copied incorrectly. I'm wondering if there is a typo in the problem itself. I too get two values for critical points. The only way that there will be only one solution for x in solving for f'(x) = 0, is the the discrimant has to be zero. IOW, ##4c^2 - 24m = 0##. If ##c^2 = 8m##, the discriminant is ##32m - 24m = 8m##.Buzz Bloom said:
One comment about the OP's work: if ##c^2 = 8m##, then it's not necessarily true that ##c = 2\sqrt{2m}##. Corrected, it would be ##c = \pm 2\sqrt{2m}##.
- #4
Mark44
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@Ameer Bux, it is frowned on here to post only images of the problem and your work. All of the work you showed can be written directly in the text window using LaTeX. We have a tutorial here: https://www.physicsforums.com/help/latexhelp/
- #5
Ameer Bux
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Mark44 said:
I'm sorry. I'll check your link and won't post it like I did the next time. Thank you
- #6
Ameer Bux
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Hi people. I emailed my teacher and he said that : C² = 6M
There was a typing error on the page.
There was a typing error on the page.
- #7
Ameer Bux
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- #8
Ameer Bux
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Got it, thanks guys
- #9
Mark44
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It's a lot simpler to NOT substitute for c^2 until later.Ameer Bux said:
If f'(x) = 0, then ##x = \frac{2c \pm \sqrt{4c^2 - 24m}}{12}##. Now, replace ##c^2## with 6m.
Related to How to Solve a Cubic Equation Involving Derivatives and Substitutions?
1. What is a cubic equation?
A cubic equation is a polynomial equation of the form ax^3 + bx^2 + cx + d = 0, where a, b, c, and d are constants and x is the variable. This type of equation has the highest degree of 3 and can have up to 3 real solutions.
2. How do I solve a cubic equation?
There are several methods to solve a cubic equation, such as factoring, using the cubic formula, or using numerical methods such as Newton-Raphson. The most efficient method will depend on the specific equation and the availability of known factors or roots.
3. Can all cubic equations be solved?
Yes, all cubic equations can be solved using the methods mentioned above. However, some equations may not have real solutions and will require the use of complex numbers.
4. What is the significance of cubic equations in science?
Cubic equations are used in many scientific fields, such as physics, engineering, and chemistry, to model and solve real-world problems. They are also important in computer graphics and animation to create smooth curves and surfaces.
5. How can I check my solution to a cubic equation?
You can check your solution by substituting the values of the variables into the original equation and seeing if it satisfies the equation. You can also graph the equation and see if the solution corresponds to the intersection points of the graph.
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