How to find the local extrema for f(x)=5x-x^2?

lilpressler083bl6

lilpressler083bl6

Answered question

2023-02-17

How to find the local extrema for f ( x ) = 5 x - x 2 ?

Answer & Explanation

buenasvistasm9xy

buenasvistasm9xy

Beginner2023-02-18Added 7 answers

Our function, which represents a parabola, can be derived, and the derivative can be set to zero: this will give us the x coordinate where the function neither increases nor decreases.
So:
f ( x ) = 5 - 2 x
set equal to zero:
5 - 2 x = 0
and:
x = 5 2
which corresponds to a y value of:
f ( 5 2 ) = 5 ( 5 2 ) - ( 5 2 ) 2 = 25 2 - 25 4 = 25 4
Graphically:
graph{5x-x^2 [-20.28, 20.28, -10.14, 10.14]}

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