# cal - Ricky Padron Say we are given the function f(x =...

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Ricky Padron Say we are given the function f(x) = 1/4x^4-x^3+7 and have to use the First and Second Derivative tests to graph f(x), f’(x), and f’’(x). We first start off by finding the first derivative of the function. Once we have the derivative we equal it to zero to get the critical points for f(x). The critical points end up being 0 and 3. We then put these numbers in a table, showing the relation of f’(x) and f(x), and choose a number less than zero, a number in between 0 and 3, and a number greater than 3. You plug these numbers into f’(x). If the result is negative the original function moves downward, and if it is positive the original function is moving upward. We get a negative number, negative number, and then positive number. This tells us that from –infinity to 3 the graph is moving downward and from 3 to infinity. We also know that 3 is a local minimum. Now we move on to the second derivative to find our inflection points and concavity. To get

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