Given the function:
Find the first derivative:
The first derivative gives us the slope of the tangent line to the graph of the function. When the tangent line is horizontal, the slope is 0, thus:
This is a quadratic equation with coefficients a = 3, b = -8, c = -7.
To calculate the solutions to the equation, we use the quadratic solver formula:
Substituting:
Operate:
Since:
We have:
There are two solutions: