The total number of cars produced by TESLA each year is y = 200000(1.25)x , where x represents the number of years after 2020. h
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We are given the following quadratic equation
The vertex is the maximum/minimum point of the quadratic equation.
The x-coordinate of the vertex is given by
Comparing the given equation with the general form of the quadratic equation, the coefficients are
a = 2
b = 7
c = -10
The y-coordinate of the vertex is given by
This means that we have a minimum point.
Therefore, the minimum point of the given quadratic equation is
If f(x) has an inverse on [a, b], then integrating by parts (take u = f(x) and dv = dx), we can show
Let . Compute the inverse:
and we immediately notice that .
So, we can write the given integral as
Splitting up terms and replacing in the first integral, we get