# cubic

1. ### Instantaneous rate of change: determining where it is positive, negative, and zero

Hi, I hope someone can help. I'm trying to find the x-coordinate for the turning point (circled in red) within my drawing: This drawing is based on the equation f(x) = x^3-2x^2+x I need to know this x-coordinate in order for me to accurately state the intervals where the rate of change is...

Competition problem here: PUZZLEUP - Weekly Puzzle Competition (a problem and games site) After a few Tylenols (extra strength), I submitted 1296: total sticks before openings : 1944 sticks removed to create openings: 648 1944 - 648 = 1296 So will I be a hero or a zero?!
3. ### How to express a cubic polynomial in general form

How to express a cubic polynomial in general form, I have a cubic polynomial as, ax3 + bx2 + cx + d = 0. How to express in general form. Suppose, If we have quadradic equation as ax2 + bx + c =0, we can express as x = -b +sqrt(b2 - 4 ac)/ 2a and -b - sqrt(b2 - 4 ac)/ 2a My question is, In...
4. ### Calculating maximum and minimum points of a cubic WITHOUT calculus

Hi everyone I wanted to ask a question about calculating maximum and minimum points. I understand it is the easiest way of calculating maximum and minimum points using differentiation. But what I wanted to ask was is it possible to calculate the maximum and minimum points of a cubic function...
5. ### Cubic question

All quadratics can be generated by transforming y= x^2. Can all cubics be generated by transforming y=x^3, my hunch tells me not but I can't see why not?
6. ### Families of Cubic Polynomial Functions

Hey :) So I just started learning how to find the rule for cubic functions but I'm really confused. Here is an attachment of one of the questions. This is what I've done so far: a) I know that this graph gives the points (-2,0) and (0,-1) So the graph sort of looks like it's in the form...
7. ### Cubic Functions

Hi everyone! I am confused on how to answer this question: Find a cubic function whose graph touches the x-axis at x= -4, cuts it at the origin and has a value 6 when x= -3 Any help much appreciated! Thank you in advance, ~ Ebony Jade :)
8. ### Cubic Functions

Hi :) I'm trying to graph some cubic functions and I know how to find the point of inflection when the equation is in turning point form, however I am unsure of how to find this point when the equation isn't in this form, for example 2x^3, I have found the x intercept is 3√5 -2 and y intercept...
9. ### Root of a cubic

Hello, I am trying to solve $x^3+2x+4=0$ over $\mathbb{R}$. My strategy is to find $s$ and $t$ such that $$3st=2$$ and $$t^3-s^3=4$$ Then $s-t$ will be one solution. My problem is, I can see that there should be only ONE real solution by considering the discriminant... but when I do the...
10. ### Inverse function of a cubic function

I have function g(x)=x^3-3x^2+3x. Is there a way to obtain the inverse function? I can do this for quadratic equations.
11. ### Is this a quadratic or a cubic?

The text I'm reading mentions this example: 3x^3 = -13x^2 + 10x. At the end it states x = 0,2/3,-5 . "Because all three of these x-values make the quadratic equation true, they are all solutions" -- There is an x^3 term, so shouldn't this equation be cubic actually as opposed to what is stated...
12. ### Cubic Substitution

In the last step it shows u^-1/2 being divided by 1/2 which made the exponent of u positive. How is that possible? Also I showed how I simplified which got me a different answer(highlighted in yellow) compared to the right answer(highlighted in green).
13. ### Have a cubic equation in terms of y, need to make it in terms of x but don't know how

Hi, The equation I need to solve for y is: 9arcsec[x] = -4y^3 -12y^2 + 16. Could anyone give me a step by step solution, or the name of an algorithm I can use to solve this problem? Thanks!
14. ### Factoring a cubic polynomial with two terms

For a fraction decomposition problem I have: 1/x3-8 and the answer book has the next step as: 1/(x-2)(x2+2x+4) I wouldn't have known this without looking in the answer book... Are there any tricks to factoring cubic polynomials like this one?
15. ### How to calculate a curvature of the cubic function.

Hi, I need some help. I have a cubic function: f(x)=ax^3+bx^2+cx+d and I need to say (to prove) which formula is better to use to calculate a curvature: k=1/R or k=f''(x)/(1+(f'(x)^2)^3/2. The answer have to be proved. Maybe there is no difference and they both give me the same result, but I...
16. ### Find equation for a graphed cubic function

I really need help with this, it's been bugging me forever. I have searched through the internet and found that to find the equation to a cubic function you can get 3 x-intercepts that pass through the x-axis and lay them out like this for example f(x)=a(x-x1)(x-x2)(x-x3) and then multiply that...
17. ### Cardano's method for depressed cubic equation

Hi, Taking this depressed cubic x^3-36x+35=0 it can easily be verified by substitution that the three roots are x=1\ \ \ \ \ \ \ x=-\dfrac{1+\sqrt{141}}{2}\ \ \ \ \ \ \ x=-\dfrac{1-\sqrt{141}}{2} My problem is, when using Cardano's method for solving a depressed cubic as outlined here...
18. ### Roots of a cubic polynomial

Hello, I am in need to know some authentic formula for finding the roots of a cubic polynomial, and to find out the conditions required for 2 complex roots and 1 real root (depending of the discriminant). Polynomial is: -a r^3 + r^2 -2 m r + Q^2=0, solve for r. Please provide me some...
19. ### find equation from graph of cubic function

I have a question asking me to draw a graph for the first and second derivatives of f(x) but I'm having trouble figuring out how to put the graphed function into an equation. I'd like to know the steps to follow they weren't outlined well in the examples of the course and I'm teaching myself...
20. ### Fibonacci's Cubic

'Sup guys. I'm new here but I'm REALLY having a hard time in my math history class. The instructor is a joke tbh. But enough about that. I need help with a couple of proofs and I've exhausted my resources. 1. The problem states: "Consider Fibonacci's Cubic x3+2x2+10x=20 a) Show that this has...