Minimizing average Cost

The cost function of a product is $C\left(x\right)=4x^3-20x^2+36x$, where $x$ is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

The cost function of a product is $C\left(x\right)=21x-12x^2+3x^3$, where $x$ is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

The cost function of a product is $C\left(x\right)=4x^3-64x^2-900x$, where $x$ is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

The cost function of a product is $C\left(x\right)=2x^2-8x+50$, where $x$ is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

The cost function of a product is $C\left(x\right)=\frac{x^3}{3}-6x^2+4x$, where $x$ is the number of units produced. In order to minimise the average cost, how many units of the product must be produced.

The cost function C of a firm is given as $\mathrm{C}=100\mathrm{x}-10{\mathrm{x}}^2+\frac{1}{3}{\mathrm{x}}^2.$Calculate output, at which the average cost is minimum. 

 The total cost of production and marketing x units of a product is given by $C\left(x\right)=\mathrm{Rs} \left(x^3-12x^2+5x+10\right)$. Find marginal cost and the number of units of the product produced to minimise the marginal cost.

 The total cost of production and marketing x units of a product is given by $C\left(x\right)=\mathrm{Rs} \left(\frac{1}{6}{x}^3-20x^2+25x+24\right)$. Find marginal cost and the number of units of the product produced to minimise the marginal cost.

If $C\left(x\right)=x^3-24x^2+600x$, find the point where $AC = MC$. Verify that $AC$ is minimum at this point. What is the minimum average cost ? 

If the cost function of a production unit is $C\left(x\right)=40-20x+10x^2$, find the average cost function and the output $x$ where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output. 
 

Find the number of units of the product produced to minimise the marginal cost when the total cost of production and marketing $x$ units of a product is given by $C\left(x\right) = Rs.\left(\frac{1}{3}{x}^3-10x^2+15x+30\right)$. 

If $C=0.01x^2+5x+100$ is the cost function for $x$ items of a product. At what level of production average cost is minimum? What is the minimum average cost? 

The total cost function for $x$ units is given by $C\left(x\right)=\sqrt{6x+5}+2500$.Find the marginal cost.

The cost function of a product is given by $C\left(x\right)=\frac{x^3}{3}-45x^2-900x+36$ where $x$ is the number of units produced. How many units should be produced to minimise the marginal cost?