MHB How to Find the Maximum of the Function f(x)=12x-32+24√(9-3x), for x≤3?

  • Thread starter Thread starter Albert1
  • Start date Start date
  • Tags Tags
    Maximum
Albert1
Messages
1,221
Reaction score
0
$f(x)=12x-32+24\sqrt {9-3x}, x\leq 3$
find $max f(x)$
 
Mathematics news on Phys.org
Albert said:
$f(x)=12x-32+24\sqrt {9-3x}, x\leq 3$
find $max f(x)$

let 9-3x = y^2 so 3x = 9-y^2 so $f(x) = 36-4y^2 - 32 + 24y = 4 - (4y^2 - 24 y) = 4 - 4(y- 3)^2 + 36 = 40 - 4(y-3)^2$
lowest when y = 3 ( range of y is >0 feasible and x = 0 so i we get 40 as maximum $f(x)$
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Similar threads

MHB Maximum and minimum of a function
Replies
1
Views
1K
MHB What is the Result of Plugging g(x) Into f(x)?
Replies
4
Views
2K
MHB How do you simplify sqrt{12x^7}?
Replies
2
Views
1K
MHB If f(3x) = f(3) + f(x) , then prove that : f(1) = f(3) =f(9) = f(27) = f(81) = 0
Replies
6
Views
2K
MHB Solve 2^3x+1=32: Find X Using Logs
Replies
5
Views
2K
MHB Fixed point,, Jacobi- & Newton Method, Linear Systems
Replies
7
Views
2K
MHB Solve √(x^2+3x+7)-√(x^2-3x+9)+2=0
Replies
5
Views
2K
MHB [ASK] polynomial f(x) divided by (x - 1)
Replies
2
Views
2K
MHB Solving Equation: x = sqrt(3x + x^2 - 3sqrt(3x + x^2))
Replies
2
Views
1K
MHB F(x) is non negative for all real x
Replies
9
Views
3K

Hot Threads

Recent Insights

Back
Top