Application of ...

The point on the curve $$y = \sqrt {x - 1}$$ where the tangent is perpendicular to the line $$2x + y - 5 = 0$$ is

The slope of the normal to the curve $$x=1-a\sin { \theta  } $$, $$y=b\cos ^{ 2 }{ \theta  }$$ at $$ \theta =\dfrac { \pi  }{ 2 } $$ is

If an edge of a cube measure $$2$$ m with a possible error of $$0.5$$ cm. Find the corresponding error in the calculated volume of the cube.

The tangents to curve $$y={ x }^{ 3 }-2{ x }^{ 2 }+x-2$$ which are parallel to straight line $$y=x$$, are

The slope of tangent to the curve $$ x=t^2 + 3t - 8, y = 2t^2 - 2t - 5 $$ at the point $$(2, -1)$$ is :

The points at which the tangent to the curve $$y = x^3 - 3x^2 - 9x + 7$$ is parallel to the x-axis are 

If $$y=8{ x }^{ 3 }-60{ x }^{ 2 }+144x+27$$ is a strictly decreasing function in the interval

If the tangent at $$(1,1)$$ on $${ y }^{ 2 }=x{ (2-x) }^{ 2 }$$ meets the curve again at $$P$$, then $$P$$ is

The tangent to the curve $$y=a{ x }^{ 2 }+bx$$ at $$\left( 2,-8 \right) $$ is parallel to $$X$$-axis. Then,

Find the critical points of the function $$f (x)= (x - 2)^{2/3} (2x + 1)$$