A quadratic function is given. f(x) = 1 + x − 7 x2 (a) Use a graphing device to find the maximum or minimum value of the quadratic function f, rounded to two decimal places. The Correct: Your answer is correct. value of f is f(x) = 1.09 Correct: Your answer is correct. . (b) Find the exact maximum or minimum value of f, and compare it with your answer to part (a).

a) , b) .

Step-by-step explanation:

a) The graphic is enclosed to the problem. By visual inspection, an absolute maximum is found.

b) The exact method consists in the application of the First and Second Derivative Tests. First and second derivatives are, respectively:

The First Derivative Test consists in equalizing the first derivative to zero and solving the expression:

According to the second derivative, the critical point leads to a maximum. The remaining component is determined by evaluation the polynomial:

The exact solution is , indicating that graphic solution leads to a good approximation.

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