For what values of \(x\) is the function \(f(x) = x^2 - 4x - 5\) increasing?

For x ∈ [ - b / ( 2a ) ; +oo ) , f is increasing; => x ∈ [ +2 ; +oo ).

Answered by crisforp | 2024-06-10

The student has asked for what values of x is the function f(x)=x²-4x-5 increasing. To determine when the function is increasing, we need to find the derivative of the function, f'(x), and analyze its behavior.
First, let's find the derivative:
The derivative of x² is 2x.
The derivative of -4x is -4.
The derivative of the constant -5 is 0.
So, the derivative f'(x) is 2x - 4. A function is increasing where its derivative is positive. Thus, we set f'(x) to be greater than zero and solve for x:
2x - 4 > 0
Add 4 to both sides:
2x > 4
Divide both sides by 2:
x > 2
Therefore, the function f(x)=x²-4x-5 is increasing for x > 2.

Answered by qwseagreen | 2024-06-24

The function f ( x ) = x 2 − 4 x − 5 is increasing for all values of x greater than 2. Therefore, the interval of increase is ( 2 , ∞ ) .
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Answered by qwseagreen | 2024-12-26