Application of ...

The slope of the tangent to the curve represented by $$x= t^{2}+3t-8$$ and $$y= 2t^{2}-2t-5$$ at the point $$M\left ( 2,-1 \right )$$ is

Two candles are of different lengths and thickness's. The short and the long ones can burn, respectively, for 3.5 hours and 5 hours. After-burning for 2 hours, the lengths of the candles become equal in length. What fraction of the long candle's height was the short candle initially?

The curve $$y= ax^{3}+bx^{2}+cx+8$$  touches $$x$$-axis at $$P\left ( -2,0 \right )$$ and cuts the $$y$$-axis at a point $$Q(0,8)$$ where its gradient is 3. The values of $$a$$, $$b$$, $$c$$ are respectively

The critical points of the function $$f\left( x \right)={ \left( x-2 \right)  }^{ 2/3 }\left( 2x+1 \right) $$ are

The graph a function $$f$$ is given. On what interval is $$f$$ increasing ?

The points of contact of the vertical tangents $$x= 2-3\sin \theta $$, $$y= 3+2\cos \theta $$ are

The fraction exceeding its $$p^{th}$$ power by the greatest number possible, where $$p\ge 2$$, is

The lines tangent to the curves $$\displaystyle y^{3}-x^{2}y+5y-2x=0$$ and $$\displaystyle x^{4}-x^{3}y^{2}+5x+2y=0$$ at the origin intersect at an angle $$\displaystyle \theta $$ equal to

A curve with equation of the form $$\displaystyle y=ax^{4}+bx^{3}+cx+d$$ has zero gradient at the point (0, 1) and also touches the x-axis at the point (-1, 0) then the values of x for which the curve has a negative gradient are

If the curve $$\displaystyle { \left( \frac { x }{ a }  \right)  }^{ n }+{ \left( \frac { y }{ b }  \right)  }^{ n }=2$$ touches the straight line $$\displaystyle \frac { x }{ a } +\frac { y }{ b } =2$$, then find the value of $$n$$.