maxima minima help (1 Viewer)

[sssona09]

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!

 

[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,



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

 

[sssona09]

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,



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

thank you!!

 

[sssona09]

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,



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

can you please help with one last one
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

 

[fan96]

can you please help with one last one
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 and , and then find in terms of . Once both sides are expressed in terms of , you can obtain a formula for area which you can then differentiate.

For reference, your area formula should be (oops!).

 

[HeroWise]

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