Discover the Relationship Between Even Functions and Modulus of Continuity

matt_747
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If f is an even function on [-a,a] , show that ω(f;[-a,a];δ) = ω(f;[0,a];ε) .

help will be appreciated so much
 
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Could you explain your notation? It's not entirely standard.
 
ω(f;[a,b];δ)= sup |f(x)-f(y)| that x,y ϵ[a,b] and |x-y|≤δ
 
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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