Tangents and it...

The slope of the tangent to the curve $$x=3t^2+1, y=t^3-1$$ at $$x=1$$ is

The point on the curve $$y=12x-x^2$$, where the slope of the tangent is zero will be

The point on the curve $$y=x^2-3x+2$$ where tangent is perpendicular to $$y=x$$ is

Any tangent to the curve $$y=2x^7+3x+5$$

The normal to the curve $$x^2=4y$$ passing through $$(1, 2)$$ is

Mark the correct alternative of the following.
The point on the curve $$9y^2=x^3$$, where the normal to the curve makes equal intercepts with the axes is?

Mark the correct alternative of the following.
The line $$y=mx+1$$ is a tangent to the curve $$y^2=4x$$, if the value of m is?

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

Consider the equation $$x^y=e^{x-y}$$
What is $$\dfrac{d^2y}{dx^2}$$ at $$x=1$$ equal to ?

Consider the equation $$x^y=e^{x-y}$$
What is $$\dfrac{dy}{dx}$$ at $$x=1$$ equal to ?