List of top Mathematics Questions on Application of derivatives asked in AP EAPCET

If \[ x+y=k,\quad x\gt 0,\quad y\gt 0, \] then \(x^2+y^2\) is minimum, if

Equation of tangent to the curve \[ y=x+\frac{4}{x^2} \] which is parallel to \(x\)-axis is

The normal to the curve \(y=f(x)\) at the point \((3,4)\) makes an angle \(\frac{3\pi}{4}\) with positive \(x\)-axis, then \(f'(3)=\)

The minimum distance of a point on the curve \[ y=x^2-4 \] from the origin is

The function \(f(x)=2x^3-9ax^2+12a^2x+1\), where \(a\gt 0\), attains its maximum and minimum at \(p\) and \(q\) respectively and \(p^2=q\). Then \(a=\)

The curve \[ y=ax^3+bx^2+cx+5 \] touches the \(x\)-axis at \(P(-2,0)\), then \(c=\)

The curves \[ y=x^2-1,\qquad y=8x-x^2-9 \]

The perimeter of a sector is constant. If its area is to be maximum, the sectorial angle should be

For a particle moving on a straight line, it is observed that the distance \(S\) at time \(t\) is given by \[ S=6t-\frac{t^3}{2} \] The maximum velocity during the motion is

If the normal drawn at a point $ P $ on the curve $ 3y = 6x - 5x^3 $ passes through the origin $(0, 0)$, then the positive integral value of the abscissa of point $ P $ is: