I've been stuck on this worksheet for days now.. we're working on derivatives now and my teacher gave us a few word problems and for most of them i think i got the correct function but am a bit doubtful when it come to my abilities (especially after my teacher told my friend behind my back that i was not reliable source )
Anyways, the first of the equations should be easy i know but i just want to check on it. Question: Find the point(s) on the graph of y= 4 - x^2 that is closest to the point(0,2)
For this one i know that we use the distance formula and the domain is all real numbers, but im not quite sure how to replace the "y" in the equation for x so that there would be only one variable.
2nd question: A rectangular page is to contain 24 square inches of print the margins at the top and at the bottom of the page are 1.5 inches each. THe margins on each side arae 1 inch. What should the dimensions of the page be so that the least amout of paper is used?
The function would be f(x) = x((24/x-2) + 3) and the derivative would be f(x)' = ((24/x-2) + 3) + x((-24/(x-2)^2)). Think the critical points are 0 and 2 not sure about the domain though.
The last question that i was not sure about is: Two posts, one 12 feet high and the other 28 feet high, stand 30 feet apart. They are to be stayed by two wires, attached to a single stake, running from the ground level to the top of each post. Where should teh stake be placed to use the least wire?
The function for this one i found out would be f(x) = sqrt(x^2 + 144) + sqrt(x^2 - 60x + 1684), but im having mad problems finding the deriviative and critical points for this one.
Any help with these would be greatly appreciated and hope the additional info helps.