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

Slope of the tangent to the curve \[ y=9x^2+7x^4+5 \] at the point \(x=1\) is

Slope of the normal to the curve \(x^{2/3}+y^{2/3}=2\) at the point \((1,1)\) is

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

Slope of the normal to the curve \(x^{2/3}+y^{2/3}=2\) at the point \((1,1)\) is

The equation of the tangent to the curve \(y=x^3\) at \((1,1)\) is

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

Let $f(x) = x^2 + 2x + 2, g(x) = - x^2 + 2x - 1 $ and $a, b$ be the extreme values of $f(x), g(x)$ respectively. If $c$ is the extreme value of $\frac{f}{g} (x)$ (for x $\neq$ 1), then $a + 2b + 5c + 4$ =