Embibe Experts Solutions for Chapter: Application of Derivatives, Exercise 1: Goa Board-2018

Variable cost of $x$ units of a commodity is $2x^2+3x$, fixed cost is$\text{ Rs. }1,800$ and total revenue of $x$ units is $9x+1808$. Find the break even point of the commodity.

The cost function of the firm is given by $C\left(x\right)=900-10x+x^2$. Find the output $x$, at which the cost is minimum.

The demand function for a product is given by $P=34+3x+\frac{27}{x}$. Find total revenue function and marginal revenue function. Also find $x$ so that the marginal revenue is equal to average revenue.

A particle moves along the curve $y=2x^3+1$. Find the points on the curve at which the $y$-coordinate changes six times as fast as the $x$-coordinate.

If the sum of the lengths of the hypotenuse and one of the sides of a right angled triangle is constant, then find the angle between that side and the hypotenuse so that the area of triangle is maximum.

Find the points on the curve $9y^2=x^3$ where normal to the curve makes equal intercepts with the coordinate axes.