The relative extrema of the function using the second derivative test where applicable is; (-9/2, -97/16)
We want to find the relative extrema of the function;
f (x) = x² + 9x − 4
To start with, we will find the derivative of the function f(x) to get;
f'(x) = 2x + 9
At f'(x) = 0, we have;
2x + 9 = 0
x = -9/2
Let us now determine if relative extrema is minimum or maximum.
Let us find the second derivative to get;
f"(x) = 2
This is greater than 0 and as such x_min = -9/2
Thus;
y_min = (-9/2)² + 9(-9/2) − 4
y_min = -97/16
Thus, the relative extrema of the function using the second derivative test where applicable is; (-9/2, -97/16)
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