Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 2: Level 2

The angle made by the tangent at any point on the curve $x=a\left(t+\sin t\cos t\right), y=a{\left(1+\sin t\right)}^2,$ with $x-$axis is

The normal to the curve $5x^5-10x^3+x+2y+6=0$ at $P\left(0,-3\right)$ meets the curve again at the point

If the point of intersection of the tangents drawn to the curve $x^{2}y=1-y$ at the points where it is intersected by the curve $x y=1-y$, is $(a, b)$, then $a+b$ is

The function $f\left(x\right)=3{\cos }^{4}x+10{\cos }^{3}x+6{\cos }^{2}x-3, 0\le x\le \pi$ is

We have three real roots of cubic equation $x^3-px+q$, where $p>0$ and $q>0$, then which of the below given statement is correct?

The total number of local maxima and local minima of the function $f\left(x\right)=x\left|x^2-x\right|+\left|x-2\right|$ is equal to

If a rectangle is inscribed in an equilateral triangle of side length $2\sqrt{2}$ as shown in the figure, then the square of the largest area of such a rectangle is _____.

Let $f\left(x\right)$ be a polynomial of degree $6$ in $x,$ in which the coefficient of $x^6$ is unity and it has extrema at $x=-1$ and $x=1$. If $\underset{x\to 0}{\lim }\frac{f\left(x\right)}{x^3}=1,$ then $5·f\left(2\right)$ is equal to