Using the Rolle's theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions :
`f(x)=x^(2)-x,x in[0,1]`

Using the Rolle's theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions : (i) f(x)=x^(2)-x, x in [0,1] (ii) f(x)=(x^(2)-2x)/(x+2), x in [-1, 6] (iii) f(x)=sqrtx-(x)/(3), x in [0,9]

Using the Rolle's theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions : f(x)=sqrtx-x/3,x in[0,1]

Using the Rolle's theorem, determine the values of x at which the tangent is parallel to the x-axis for the following functions : f(x)=(x^(2)-2x)/(x+2),x in[-1,6]

Using the Rolle's theorem, determine the value of x at which the tangent is parallel to the x-axis for the following functions: f(x) = sqrtx - (x)/(3), in [0,9]

Using the Lagrange's mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval: f(x)=x^(3)-3x+2,x in[-2,2]

Using the Lagrange's mean value theorem determine the values of x at which the tangent is parallel to the secant line at the end points of the given interval: f(x)=(x-2)(x-7),x in[3,11]

The point of curve y= 2x^(2) - 6x -4 at which the tangent is parallel to x-axis is

Using Rolle's theorem find the point on the curve y=x^(2)+1,-2lexle2 where the tangent is parallel to x-axis.