From the given two options, none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
What is a function?
A function is a correspondence between input numbers (x-values) and output numbers (y-values). It is used to describe an equation.
Given that:
Suppose that x = c is a critical point of (x) then,
If f'(x) > 0 to the left of x = c and f'(x) < 0 to the right of x = c;
- then x = c is a local maximum.
If f'(x) < 0 to the left of x = c and f'(x) > 0 to the right of x = c;
- then x = c is a local minimum.
If f'(x) is the same sign on both sides of x = c;
- then x = c and is neither a local maximum nor a local minimum.
From the given equation, the critical points: x = -3
- The intervals is: Increasing at -∞ < x < -3 and decreasing at -3<x<∞
If we put the point x = -3 into - |x+3|-2
- Then, y = -2 and it is Maximum at (-3, -2)
- Only f(x) = (x+3)^2 - 2 has a minimum at (-3,-2)
We can therefore conclude that none of them has a function that has the same maximum value as f(x) = -|x+3|-2.
Learn more about the maximum and minimum of a function here:
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