isi-entrance 2018 Q5

isi-entrance · India · UGA Stationary points and optimisation Find critical points and classify extrema of a given function

Let $f ( x )$ be a degree 4 polynomial with real coefficients. Let $z$ be the number of real zeroes of $f$, and $e$ be the number of local extrema (i.e., local maxima or minima) of $f$. Which of the following is a possible $( z , e )$ pair?
(A) $( 4,4 )$
(B) $( 3,3 )$
(C) $( 2,2 )$
(D) $( 0,0 )$

Let $f ( x )$ be a degree 4 polynomial with real coefficients. Let $z$ be the number of real zeroes of $f$, and $e$ be the number of local extrema (i.e., local maxima or minima) of $f$. Which of the following is a possible $( z , e )$ pair?\\
(A) $( 4,4 )$\\
(B) $( 3,3 )$\\
(C) $( 2,2 )$\\
(D) $( 0,0 )$

Paper Questions

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