Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: AMU-AT (B.Tech.) 2017

A particle is moving along the curve $x=a{t}^2+bt+c$. If $ac=b^2,$ then the particle would be moving with uniform

If $f\left(x\right)=x{e}^{x\left(1-x\right)},$ then $f\left(x\right)$ is

The equation of the normal to the curve $y=e^x$  at $\left(0, 1\right)$ is

The length $x$ of a rectangle is decreasing at the rate of $6 \mathrm{cm}/\min$ and the width $y$ is increasing at the rate of $4 \mathrm{cm}/\min .$ When $x=8 \mathrm{cm}$ and $y=4 \mathrm{cm},$ the rate of change of the area of the rectangle (in ${\text{cm}}^2/\text{min}$) is

The total revenue in rupees received from the sale of $x$ units of a product is given by $R\left(x\right)=5x^2+20x+7.$ The marginal revenue, when $x=8$ is

The function $f\left(x\right)=\cos x$ is strictly decreasing on