Question

A curve with equation of the form $y=a{x}^4+b{x}^3+c+cx+d$ has zero gradient at the point (0,1) and also touches the x-axis at the point (-1, 0) then the values of the x for which the curve has a negative gradient are :

• A. $x>-1$
• B. $x<1$
• C. $x<-1$
• D. $-1\le x\le 1$

Answer 1

The correct option is C $x<-1$

$\frac{dy}{dx}{|}_{x=0}=4a{x}^3+3b{x}^2+c=0$
$\therefore c=0$
$\frac{dy}{dx}<0$
$4a{x}^3+3b{x}^2<0$
$x^2(4ax+3b)<0$
$x<-\frac{3b}{4a}$