Help (1 Viewer)

[Arithela]

1. Find the maximum value of 5x - 2x^2

 

[undalay]

let f(x) = 5x - 2x^2
f'(x) = -4x + 5
set f'(x) = 0
-4x + 5 = 0
x = 5/4

f''(x) = -4
f"(5/4) = -4
-4<0, thus at x = 5/4, a maximum TP occurs.
f(5/4) = 25/4 - 2(25/16)
f(5/4) = 25/8

Thus the maximum value is 25/8

 

[zingerburger]

Let's see...

- Derivitate it and you should get 5-4x i.e. first derivative is 5-4x or y' = 5-4x.
- Derivativise it again and you should get -4 i.e. second derivative is -4 or y'' = -4
- For a maximum, it must be stationary (first derivative = 0) and concave down (second derivative < 0)
- Therefore y' = 0 i.e. 5-4x = 0.
- 4x = 5
- x = 5/4.
- When x = 5/4, y = 5 * 5/4 - 2 * 5/4^2.
- Push buttons on the calculator and y = 3 and 1/8 i.e. coordinates of stationary point are (1 and 1/4,3 and 1/8)
- Since y" = -4, which is less than 0, it's concace down.
- Therefore maximum is at (1 and 1/4,3 and 1/8).

It's been a long while since I've done maths questions but that should be right.

EDIT: Damn it. I go off to do something else and undalay beats me to it.