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

In a regular triangular prism, the distance from the centre of one base to one of the vertices of the other base is $l$. The altitude of the prism, for which the volume is greatest, is:

Let $P\left(x\right)=a_0+a_1{x}^2+a_2{x}^4+\mathrm{......}+a_n{x}^{2n}$ be a polynomial in a real variable $x$ with $0<a_0<a_1<a_2<\mathrm{......}<a_n$. The function $P\left(x\right)$ has

If $g\left(x\right)=7x^2{e}^{-x^2}, \forall x\in R$, then $g\left(x\right)$ has

The coordinates of the point on the parabola $y^2=8x$, which is at minimum distance from the circle $x^2+{\left(y+6\right)}^2=1$ are

Let $S$ be the set of real values of parameter $\lambda$ for which the function $f\left(x\right)=2x^3-3\left(2+\lambda \right)x^2+12\lambda x$ has exactly one local maxima and exactly one local minima. Then the subset of $S$ is-

The value of '$a$' for which the function $f\left(x\right)=\left\{\begin{array}{cc}-x^3+{\cos }^{-1}a,& 0<x<1\\ x^2,& x\ge 1\end{array}\right.$ has a local minimum at $x=1$, is

If a continuous function $f\left(x\right)$ has a local maximum at $x=a$, then

On the ellipse, $4x^2+9y^2=1$, the points at which the tangents are parallel to the line $8x=9y$ are -