Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0

mortysmith

New member
Joined
Jul 14, 2019
Messages
1
Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0
I'm trying to solve this problem but can't. Can anybody help me providing a solution please?
 
Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0
I'm trying to solve this problem but can't. Can anybody help me providing a solution please?
Please follow our procedure of posting problem at this forum - enunciate at:


Hint: What is the derivative of f(x) w.r.t. 'x'?

How is the derivative related to the maximum value?
 
Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0
I'm trying to solve this problem but can't. Can anybody help me providing a solution please?
Please be specific about where you got stuck. There are several possibilities for what you might have done wrong or been unable to do, and our goal is to help you find that error, not just to give a full answer. (There is no special trick to this problem.)
 
Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0
I'm trying to solve this problem but can't. Can anybody help me providing a solution please?
I would find the x-value for the max (and min) using the formula x=[-b +/- sqrt(b^2 - 3ac)]/(3a)
This can be very helpful depending on the value for x in the step above.
If the larger of the two x's is positive or 0 what does that tell you about the max for f(x)??
If the larger of the two x values is negative what does that tell you about the max for f(x)?
 
I would [use] the formula x=[-b +/- sqrt(b^2 - 3ac)]/(3a) … If the larger [x-value] is negative what does that tell you about the max …
That was my thought (or use a graphing calculator) and maybe it was Jeff's thought, too, because morty posted on the Intermediate Algebra board. Yet, I would ignore the negative x-value (because the problem implies that x is non-negative at the local maximum).

@mortysmith \(\;\) Here's more information about the formula (post #5) for finding x-values at the local min and max of the cubic polynomial ax^3+bx^2+cx+d.

?
 
That was my thought (or use a graphing calculator) and maybe it was Jeff's thought, too, because morty posted on the Intermediate Algebra board. Yet, I would ignore the negative x-value (because the problem implies that x is non-negative at the local maximum).

@mortysmith \(\;\) Here's more information about the formula (post #5) for finding x-values at the local min and max of the cubic polynomial ax^3+bx^2+cx+d.

?
Otis, I think that you are missing my point. If the local maximum occurs when x is negative then the max on the restricted domain (x>0) will occur at x=0.
 
Find the maximum value of the function f(x) = x + x^2 − x^3 for x ≥ 0
I'm trying to solve this problem but can't. Can anybody help me providing a solution please?
I assume that you know basic calculus.
\(\displaystyle f(x)=x+x^2-x^3\\f'(x)=1+2x-3x^2\\f"(x)=2-6x\)
A local maximum point occurs at \(\displaystyle x_0\) for which \(\displaystyle f'(x_0)=0~\&~f"(x_0)<0\)
You post what you find.
 
@ pka As far as I am concerned, the key issue in this thread is whether the OP has a clue about calculus. The thread was initiated in algebra. Jomo's formula is indeed easily derived from calculus, but it is likely to be a deus ex machina to an algebra student. As Dr. P and otis have said, it can be solved without calculus, but the solution is not so obvious.

However, the whole thing appears moot as the OP has not responded to the subsequent posts.
 
… it can be solved without calculus, but the solution is not so obvious.

However, the whole thing appears moot as the OP has not responded …
Agree, on both counts. The formula would need to be taught (if used in algebra class). And we don't know, yet, what methods morty's been taught.
\[\;\]
 
Top