Find the value of x at which the function has a possible relative maximum or minimum point. (Recall that ex is positive for all x.) Use the second derivative to determine the nature of the function at these points. f(x) = (7+ x) e - 4x What are the first and second derivatives of f(x)? f'(x) = f"(x) =

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A: Please refer to the image below.

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: