Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: Nagaland Board-2020

Find the coordinates of the point at which the tangent to the curve $f\left(x\right)=x^2-6x+1$ is parallel to the chord joining the points $(1,-4)$ and $(3,-8)$

Show that the semi vertical angle of a cone of maximum volume and given slant height is ${\tan }^{-1}\sqrt{2}$.

Prove that the volume of the largest cone that can be inscribed in a sphere of radius of $\mathrm{R}$ is $\frac{8}{27}$ of the volume of the sphere.

The slope of the normal to the curve $y=2x^2+3\sin x$ at $x=0$ is

Find the equation of the tangent to the curve $y=\sqrt{3x-2}$ which is parallel to the line $4x-2y+5=0$.

A ladder $5 \mathrm{m}$ long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of $2 \mathrm{cm}/\mathrm{s}$. How fast is its height on the wall decreasing when the foot of the ladder is $4 \mathrm{m}$ away from the wall?

Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.

Show that semi-vertical angle of right circular cone of given surface area and maximum volume is ${\sin }^{-1}\left(\frac{1}{3}\right)$.