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

If the sum of length of the hypotenuse and another side of a right-angled triangle is given. The area of the triangle is maximum when the angle between them is

The equation of tangent at those points where the curve $y=x^2-3x+2$ meets  $x$-axis are

The curve $y+e^{xy}+x=0$ has a tangent parallel to the $y$-axis at the point

In a culture the bacteria count is $1,00,000$. The number is increased by $10\%$ in $2$ hours. In how many hours will the count reach $2,00,000$, if the rate of growth of bacteria is proportional to the number present.

Note$:$ Assume base of logarithm as $e$.

If $f\left(x\right)=x^3+a{x}^2+bx-5{\cos }^{2}x$ is an increasing function for all real values of $x,$ then $a,$ and $b$ satisfy the condition

The maximum area of a rectangle of perimeter $176 \mathrm{cms}$ is

If $S$  is the set, such that  $f\left(x\right)=8x^2-\ln \left|x\right|$ is increasing in $S$, then $S$ contains

The maximum value of $f\left(x\right)=|x\ln x|$in $x\in (0,1)$ is