tmua.me Extreme Set B Paper 2 · Question 15

Let

f(x)=x^4-\frac32x^2,

and let $k$ be a real constant. Consider the statements

S: For every real number $h>0$ , the equation

$\displaystyle f(x+h)-f(x)=kh$

has exactly one real solution for $x$ .
T: $k<-1$ or $k>1$ .

Is S necessary and/or sufficient for T?

AS is neither necessary nor sufficient for T

BS is necessary but not sufficient for T

CS is sufficient but not necessary for T

DS is necessary and sufficient for T

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