If (-1,2) and and (2,4) are two points on the curve y=f(x) and if g(x) is the gradient of the curve at point (x,y) then the value of the integral `int_(-1)^(2) g(x) dx` is

The points on the curve y=12x-x^3 at which the gradient is zero are

At the point (2,3) on the curve y = x^(3) - 2x + 1 , the gradient of the curve increases

At the point (2, 5) on the curve y=x^3-2x+1 the gradient of the curve is increasing

Find the point on the curve y=x^3+x^2+x at which the tangent to the curve is perpendicular to the x+y=1

Consider f(x)=int_(1)^(x)(t+(1)/(t))dt and g(x)=f'(x) If P is a point on the curve y=f(x) such that the tangent to this curve at P is parallel to the chord joining the point ((1)/(2),g((1)/(2))) and (3,g(3)) of the curve then the coordinates of the point P

The slope at any point of the curve y = f(x) is given by (dy)/(dx)= 2x it passes through (1,-1) then the equation of the curve is :

Consider f(x)=int_1^x(t+1/t)dt and g(x)=f'(x) If P is a point on the curve y=g(x) such that the tangent to this curve at P is parallel to the chord joining the point (1/2,g(1/2)) and (3,g(3)) of the curve then the coordinates of the point P