NCERT Solutions for Chapter: Application of Derivatives, Exercise 1: EXERCISE

At what points on the curve $x^2+y^2-2x-4y+1=0$ the tangents are parallel to the $y$ -axis?

At what point, the slope of the curve $y=-x^3+3x^2+9x-27$ is maximum? Also find the maximum slope.

Find the points of local maxima, local minima and the points of inflection of the function $f\left(x\right)=x^5-5x^4+5x^3-1$. Also find the corresponding local maximum and local minimum values.

Find the dimensions of the rectangle of perimeter $36 \mathrm{cm}$ which will sweep out a volume as large as possible, when revolved about one of its sides. Also find the maximum volume.

The sum of the surface areas of a rectangular parallelepiped with sides $x, 2x$ and $\frac{x}{3}$ a sphere is given to be constant. Prove that the sum of their volumes is minimum, if $x$ is equal to three times the radius of the sphere. Also find the minimum value of the sum of their volumes.

The curves $y=4x^2+2x-8$ and $y=x^3-x+13$ touch each other at the point _____

The values of $a$ for which the function $f(x)=\sin x-ax+b$ increases on $\mathrm{R}$ are _____.

The function $f\left(x\right)=\frac{2x^2-1}{x^4},x>0$ decreases in the interval _____.