find 2 numbers whose sum is 54 and whose product is a maximum (using calculus)?
Obviously the 2 numbers are 27 and 27 but how do I prove that using calc
- Φ² = Φ+1Lv 73 weeks ago
Let our two number be a and b such that a = 27+x and b = 27-x, so a+b=54 and ab = 27² - x².
The maximum value occurs when x² = 0, so when x = 0 a = b = 27.
- Michael ELv 73 weeks ago
You have a number x
You want to maximize x(54-x)
create a function y = 54x - x^2
dy/dx = 54 - 2x
x = 27 is where dy/dx = 0, from there determine whether it is a maximum or a minimum.
- no sea naboLv 63 weeks ago
Using ax²+bx+c=0 solve x₁ and x₂
now x₁+x₂=-(b/a) and x₁.x₂=(c/a)
S=x₁+x₂ and P=x₁.x₂
when derive by λ:
2λ-S=0 (maximum or minimum) λ=S/2