Question

Calc 1 Help?

Answer 1

The difference between two numbers is 24. If both numbers are 100 or greater, what is the minimum value of their product?

Answer 2

First, select letters to represent the 2 quantities (numbers). How would you represent symbolically (with an equation) that the difference between them is 24?

Answer 3

@mathmale
x-y=24
than:
x=24+y

Answer 4

(larger number) - (smaller number) = 24. Represent this symbolically.

How would you then represent the product of these two unknown numbers?

Hint: Mult the larger number by the smaller, representing this product symbolically.

Since you're in calculus, you know the standard approach to maximizing / minimizing a function: find the first derivative of the function after you have expressed it depending on only one variable (not both), set this derivative = to 0, and solve for that variable. Your result is called a "critical value." What next?

You could also graph the function mentioned above, and then look ONLY at x-values equal to or greater than 100. For which such value is the product of these 2 numbers a min?

Answer 5

Hmm this one has me a bit stumped.
I can't figure out how to deal with the "both greater than 100".

If each value is larger than 100,
then their product is at least 100*100.

\(\large\rm xy>10000\)

I wonder if that will help.. hmm..
still not sure

Answer 6

the graph of the derivative is a parabola , so yeah i think it is just the value 100 and 124

Answer 7

@zepdrix @mathmale
Thanks. So... I guess I actually set this up wrong. I was trying to minimize the bigger number.. & the domain
x-y=24
y=x-24
Domain: x greater than/equal to 124 (bigger number)
f(x)=xy
f(x)=x(x-24)
f(x)=x^(2)-24x
f'(x)=2x-24
Critical Point @ x=12
But end point @ 124 so:
y=100
x=124

Answer 8

suppose smallest number is 100 then other number is 124
product 124*100=12400
so

Answer 9

@DanJS yep lol hahah
&@sshayer thanks

Answer 10

np