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How to draw the graph of $8x^3 -6x+1=0$?

Any generalization of a graph of polynomials of degree 3 is helpful.

Rhea
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  • You can use Wolfram Alpha to plot $$8x^3-6x+1$$ – Dr. Sonnhard Graubner May 11 '19 at 16:05
  • Usually, you create a value-table. If you know the critical points and the roots, you can already estimate how the graph will look like. – Peter May 11 '19 at 16:08
  • @Peter I want to determine the range of the roots from the graph. So, can you please elaborately explain how to draw it? – Rhea May 11 '19 at 16:12
  • https://math.stackexchange.com/questions/2157643/how-can-i-solve-the-equation-x3-x-1-0 and https://math.stackexchange.com/questions/2203364/solve-the-following-equation-x3-3x-sqrtx2 – lab bhattacharjee May 11 '19 at 16:16
  • @Rhea If you find values $x_1$ and $x_2$ such that $f(x_1)$ and $f(x_2)$ have distinct signs , then you can conclude that there must be at least one root between $x_1$ and $x_2$. To estimate the roots ONLY from a graph, a value table with sufficiently many $x$-values is usually the best way. – Peter May 11 '19 at 16:20

1 Answers1

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A good method I use to plot graphs:

A) Domain

B) Intercepts $x,y=0?$

C) Symmetry/Periodicity:

Symmetry: If $f(-x)=f(x)$ on the domain then it is EVEN (symmetric about y axis).

Or $f(-x)=-f(x)$ on domain then it is ODD (symmetric about the origin).

Can be neither odd or even.

Periodicity: Where $f(x+p)=f(x)$ where $p$ is a positive constant.

D) Asymptotes (horizontal/vertical)

E) Intervals of increase or decrease ($f'(x)$)

F) Local Min/Max or Inflection ($f'(x)=0$)

G) Concavity ($f''(x)$)

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    If you need any more details then please let me know I can elaborate! –  May 11 '19 at 16:17