Linear functions/translation of graphs

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The discussion centers on analyzing the function f(x) = x^3 - 3x for critical points and symmetry. It is established that the function can be factored to find its roots, specifically x(x^2 - 3), which leads to the values of x that make f(x) = 0. The conversation also touches on the criteria for symmetry, questioning whether f(x) is even or odd by evaluating f(-x). The function exhibits odd symmetry since f(-x) = -f(x). Overall, the analysis seeks to understand the behavior of the cubic function in terms of its critical points and symmetry properties.
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The question is

Graph f(x)=X^3-3x. Does it have any high or low points? What about symmetry?

Okay the problem I'm having is what formula to use with a ^3 on the X, my previous 2 problems I did by using the quad formula, those questions were f(x)= 2x^4+4x^2-1, and f(x)= 16x^2+4x-3 respectively.
 
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f(x)= x^3- 3x= x(x^2- 3). What values of x makes f(x)= 0? What happens between those values of x?
 
What about symmetry?

f(x) = f(-x)?

f(-x) = -f(x)?
 

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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