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?
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.