How do calculate the maximum of this function: 100x-3x^2/10?

Question

Please help, thanks.

Answer 1

If

f(x) = 100x - 3x^2/10, then
f'(x) = 100 - 3x/5

To get the maximum of the function, make f'(x) = 0
0 = 100 - 3x/5
3x/5 = 100
3x = 500
x = 500/3

So your critical value is x = 500/3. To determine whether it's a maximum, you have to test the behavior from (-infinity, 500/3] and [500/3 to infinity].

Let's test a number from the first interval (x = 0).
Then f'(0) = 100 - 0 = 100, which is a positive number. Therefore, f is increasing on (-infinity, 500/3]

Let's test a number from the second interval (x = a million)
Then f'(a million) = [something smallish] minus [something super big divided by 10]. You'll find that this gives a negative number.
Therefore, f is decreasing on [500/3, infinity)

This means that x = 500/3 is indeed a maximum. If you wanted to calculate the maximum (which is required especially in optimization problems), all you have to do is calculate f(500/3).

Answer 2

Rewrite it a little:

y = (-3x²+100x) / 10

This is clearly a parabole with its legs downwards.
So the maximum is in the top op the parabole.
The top for a parabole ax²+bx+c is always -b/2a.
So in this case the maximum is at position x = 100/6.
Fill this in and find: y = 500/3.

If you mean:
y = - 3/10 x² + 100 x then
x = 1000 / 6 = 500 / 3
y = 2500 / 3

Answer 3

1) Differentiate y=100x-3x^2/10 with respect to x.
You'll get dy/dx=100-3x/5

Let dy/dx=0,
100=3x/5
x = 166 and 2/3 = 166.6666...

To check if value is the maximum, differentiate dy/dx once more with respect to x.
d2y/dx2=-3/5<0

Which proves that x=166.666... gives the maximum value.

Hence, the maximum of this function can be found out by substituting x=166.66... into y=100x-3x^2/10
Therefore, the maximum of the function = 8333.333 = 8333 and 1/3.

Answer 4

Hope u know differential calculus to understand the folowing.

let f(x) be 100x-3x^2/10
differentiate it and solve for x..
i ll call the first differential as f'(x).. Solve it as f'(x)=0
which is 100-3x/5 = 0 ==>> x=166.667
if u had got more than one solution, what u hav to do is differentiate the equation once more..which would result in -3/5
the answer being negative signifies a maximum of the function.
the answer is 166.667 substituted in the original equation. you ll get the solution 8333.333333333

Answer 5

-3x²/10 + 100 = 0
If a < 0, then to x = -b/2a, the maximum of this function is:
Yv = -100/2(-0,3) = 50.10/3 = 500/3 = 166,6

Ok?

Answer 6

Find the derivative of your function
Find the roots of that derivative.
calculate the value of the function for each root.