-2
$\begingroup$

1) GetThere Airlines currently charges $200$ dollars per ticket and sells $40{,}000$ tickets a week. For every $10$ dollars they increase the ticket price, they sell $1000$ fewer tickets a week. How many dollars should they charge to maximize their total revenue?

2) What is the smallest distance between the origin and a point on the graph of $y=\dfrac{1}{\sqrt{2}}\left(x^2-3\right)$?

How would I do these two problems?

  • 0
    Hi, welcome to Math.SE. Please indicate what you have tried, your thoughts on the problem and where you got stuck. This will help people better tailor their answer to your background and situation. It will also demonstrate that you are interested in your question and not just looking for someone to do your homework for you - Math.SE is not a homework site. $$$$ Also split your two questions into two separate posts. – 2017-01-22

1 Answers 1

2

answer to the second question:

A point on the curve is given by: $$({x,\frac{{1}}{\sqrt{2}}\cdot(x^2-3)})$$

distance of a point on the curve from origin is given by:

$$D= \sqrt{x^2 + \frac{1}{2}\cdot(x^2-3)^2}$$

differentiate w.r.t $x$ and equate it to zero and simplify the equation to $x(x^2-3x+1)=0$ and find $x$ to get minima.

  • 0
    calculation part is skipped for you to solve yourself. – 2017-01-22