Algebra: Minima, Maxima, Circles. [closed]

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?

closed as off-topic by Ian Miller, Rohan, астон вілла олоф мэллбэрг, pjs36, LeucippusJan 22 '17 at 6:13

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• 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. – Ian Miller Jan 22 '17 at 4:12

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