A certain drug is made from only two ingredients: compound A and compound B. There are 5 milliliters of compound A used for ever
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Zeroes:
We must solve
To do so, we define the auxiliary variable . The equation becomes
The quadratic formula yields the solutions
Substituting back gives
So, the zeroes are -6, -3, 3, 6.
Turning points:
Turning points are points where a function stops being increasing to become decreasing, or vice versa. Since functions are increasing when their first derivative is positive and decreasing when it's negative, turning points are points where the first derivative is zero.
We have
If we set the derivative to be zero, we have
So, the derivative is zero if x=0 or