Using derivatives, it is found that:
- The function is increasing on the interval [-8,0].
- The function is decreasing on the interval [0,8].
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The first step is finding the critical points of f(x), which are the points in which [tex]f^{\prime(x)} = 0[/tex]
The function is: [tex]f(x) = -x^2 + 4[/tex].
Thus, the derivative is:
[tex]f^{\prime}(x) = -2x[/tex]
The critical point is:
[tex]-2x = 0 \rightarrow x = 0[/tex]
- For x < 0, [tex]f^{\prime}(x) > 0[/tex], thus, the function increases in the interval [-8,0].
- For x > 0, [tex]f^{\prime}(x) < 0[/tex], thus, the function decreases in the interval [0,8].
- The graph appended at the end of this answer corroborates this.
A similar problem is given at https://brainly.com/question/13539822
