Tangents and it...

The equation of the tangent to the curves $$x=t\cos t$$ and $$y=t\sin t$$ at the origin is?

Let $$f(x)=2{ x }^{ 3 }-5{ x }^{ 2 }-4x+3,\cfrac { 1 }{ 2 } \le x\le 3$$. The point at which the tangent to the curve is parallel to the X-axis is

The equation of the tangent to the curve $$y={ x }^{ 3 }-6x+5$$ at $$(2,1)$$ 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

The equation of the tangent to the curve $$y=4e^{-x/4}$$ at the point where the curve crosses Y-axis is equal to

The equation of tangent of the curve $$y = be^{-x/a}$$ at the point, where the curve meet y-axis is

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 

The slope of the tangent to the curve $$y=3{ x }^{ 2 }-5x+6$$ at $$\left( 1,4 \right) $$ is