maxima minima help

• 7 Dec 2017, 5:33 PM
sssona09
maxima minima help
heey guys how would I do these
1. The revenue from a company's product is given by R=180m+42m^2-m^3 where m is the output (per unit of time). Determine the output that will give maximum revenue.

2. An objet is projected into the air. The height of the object after t seconds is given by h=60t-5t^2
(I) what is the maximum height the object reaches?
(ii) how long after reaching the maximum height is the object 100m above its starting level?

for 2i I got 180m? is it right? dunno the rest :(

thank you all!
• 7 Dec 2017, 5:46 PM
integral95
Re: maxima minima help
1. you find dR/dm (differentiate with respect to m), then let it equal to 0 and solve for m, make sure that the solution is positive.

2.i 180 is correct.

2ii) you have to solve the equation,

$60t-5t^2 = 100$

The answer has to be greater than 6 since it occurs after reaching the maximum height.
• 7 Dec 2017, 6:00 PM
sssona09
Re: maxima minima help
Quote:

Originally Posted by integral95
1. you find dR/dm (differentiate with respect to m), then let it equal to 0 and solve for m, make sure that the solution is positive.

2.i 180 is correct.

2ii) you have to solve the equation,

$60t-5t^2 = 100$

The answer has to be greater than 6 since it occurs after reaching the maximum height.

thank you!!
• 7 Dec 2017, 6:00 PM
sssona09
Re: maxima minima help
Quote:

Originally Posted by integral95
1. you find dR/dm (differentiate with respect to m), then let it equal to 0 and solve for m, make sure that the solution is positive.

2.i 180 is correct.

2ii) you have to solve the equation,

$60t-5t^2 = 100$

The answer has to be greater than 6 since it occurs after reaching the maximum height.

A piece of wire 20cm in length is bent to form a rectangle. Find the dimensions of the rectangle so as to enclose maximum area
• 7 Dec 2017, 7:39 PM
fan96
Re: maxima minima help
Quote:

Originally Posted by sssona09
A piece of wire 20cm in length is bent to form a rectangle. Find the dimensions of the rectangle so as to enclose maximum area

The perimeter of the rectangle is obviously 20cm. Let the sides be $x$ and $y$, and then find $y$ in terms of $x$. Once both sides are expressed in terms of $x$, you can obtain a formula for area which you can then differentiate.

For reference, your area formula should be $A = 10x-x^2$ (oops!).
• 9 Dec 2017, 12:16 AM
HeroWise
Re: maxima minima help
https://i.imgur.com/Mqy5Qiw.jpg
https://i.imgur.com/Ng4uWh1.jpg
https://i.imgur.com/O3oVcMb.jpg

Im learning too so i just planned to give it a try and post the working out for people who might need help