1.Determine the maximum area of a triangle that has a hypotenuse of 5 m.[/FONT][/COLOR]
2.Determine the local maxima and local minima of the function sinx^3 +cosx^3 for (0,2pie)
3. Two sides of a triangle have lengths of 1 m and 2 m. The angle between them is increasing at /1000 rad/s.Determine the rate of change of the third side when the angle between the first two sides is pie/4
For the first exercise, let x be one of the sides of the triangle.
Then, express the length of the third side with respect to the hypotenuse and x, using the Pythagorean theorem.
--> area=x*(third side)/2=...a function of x...
Edit : this is my 22th post ^^
The area of this triangle is
Use the first derivative to find the value of a that corresponds to the maximum area.