The function \( f(x)=2 x^{3}+\alpha x^{2}+\beta x+r \) where \( \alpha, \beta, r \in R \) has lo...

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The function \( f(x)=2 x^{3}+\alpha x^{2}+\beta x+r \) where \( \alpha, \beta, r \in R \) has local minima at \( x=3^{t} \) and local max at \( x=2.3^{t} \). If \( x=\frac{5}{2} \) is the point of inflection then the possible value of \( t \) is \( \log _{3} k \). Where \( k \) is
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