The function that is a tangent to the graph of f is
The definite integral can be interpreted as the resulting area of a region. In addition, it is a value in its result, that is, it does not depend on the variable x, which can be exchanged for any other variable without changing the value of the integral.
Knowing that :
- 40x + y = 0 is tangent of f(x)
- slope of the line = -40
therefore, f'(x)|x=a = -40, so only look for a we have:
if, x = -2, then y = 80 (since, 40x + y = 0), therefore, f(x) passes through (-2,80), so in the equation:
Therefore,
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