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

A curve with equation of the form `y=a x^4+b x^3+c x+d`has zero gradie

1.	A curve with equation of the form `y=a x^4+b x^3+c x+d`has zero gradient at the point `(0,1)`and also touches the `x-`axis at the point `(-1,0)`then the value of `x`for which the curve has a negative gradient are:`xgeq-1`b. `x
Answer» Correct Answer - C We have , `(dy)/(dx)=0 ` at (0,1) and (-1,0) ` therefore c=0 " and " -4a+3b -c=0 rArr a=(3b)/(4) " and " c=0 " "...(i)` Also, the curve passes through (0,1) and (-1,0) ` therefore d=1 and 0=a-b-c+d rArr a-b-c+1 =0 " "...(ii)` From (i) and (ii), we get `a=3, b=4,c=0 and d=1 ` ` therefore y=3x^(4)+4x^(3)+1 rArr (dy)/(dx)=12x^(3)+12x^(2) ` Now, `(dy)/(dx) lt 0 rArr 12x^(3)+12x^(2) lt 0 rArr x+1 lt 0 rArr x lt -1 `

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