Question

CALCULUS MAXIMA MINIMA PROBLEMS

Answer 1

\[\fbox{1}\text{ A trianlge has a prescribed perimeter } \\2S \text{ deteremine the sides of the trangle as to maximise area}\\ \fbox{2}\text{ A triangle is such that the product of the sines of its angles is a maximum,show that the triangle is equilateral}\]
\[\fbox{3}\text{ Given }\\ mx+ny=0\\ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\\text{find the minimum distance to the origin,for a point on both the line and the ellipse}\\ \fbox{4}\text{if the condition is given that}x+y=1,\text{find the maximum of}\\ax^p+by^p,0<p<1,a,b>0\]

Answer 2

You're given a function f(x) to find its maxima and minima.

You can use f'(x)=0 to solve for x to find its extrema.

Then plug the extrema into f''(x) to see if it's a maximum or a minimum. If f''(x) is positive, it's a minimum. If f''(x) is negative, it's a maximum.

Answer 3

2) show that the triangle is equilateral

Answer 4

Sorry, I don't know how to do :/