If the slope of tangent to a curve y=f(x...

If the slope of tangent to a curve `y=f(x)` is maximum at `x=1` and minimum at `x=0`, then equation of the curve which also satisfies `(d^3y)/dx^3=4x-3`, is (A) `y=x^4/6-x^3/2+x^2/2+1` (B) `y=x^4/4+x^3-x^2/3+1` (C) `y=x^4/4-x^3/7+x^2/3+3` (D) none of these

Similar Questions

Explore conceptually related problems

Slope of the tangent to the curve y=3x^(4)-4x at x=1 is 6.

Find the slope of tangent to the curve y = 4x^2 - 3x +7 at The point whose x-coordinate is 3.

The slope of the tangent to curve is (xy^2+y)/x and it intersects the line x+2y=4 at x=-2. If (3,y) lies on the curve then y is

Find the length of the tangent for the curve y=x^(3)+3x^(2)+4x-1 at point x=0.

The maximum slope of the curve y=-x^(3)+3x^(2)-4x+9 is

Find the slope of the tangent to the curve y=3x^(2)-4x at the point, whose x - co - ordinate is 2.

The equation of the locus of points which are equidistant from the points (2,-3) and (3,-2) is (A) x+y=0 (B) x+y=7 (C) 4x+4y=38 (D) x+y=1

(6) 2x-3y=4 ; 3y-x=4

If the equation of tangent to the circle x^(2)+y^(2)-2x+6y-6=0 and parallel to 3x-4y+7=0 is 3x-4y+k=0 then the values of k are

The normal to the curve x^(2)=4y passing (1,2) is (A) x+y=3 (B) x-y=3 (D) x-y=1