Final answer:
The quadratic function f(x) = 2x² - 5x - 7 has a minimum value rather than a maximum because the coefficient of the x² term is positive.
Step-by-step explanation:
The function f(x) = 2x² - 5x - 7 is a quadratic function, which has the general form ax² + bx + c. The coefficient of the x² term is positive, indicating the parabola opens upwards.
Thus, this quadratic function has a minimum value at its vertex. To determine whether f(x) has a maximum or minimum, one can use the vertex formula, h = -b/2a, or take the second derivative. If the second derivative is positive at a point, the function has a minimum there; if it is negative, the function has a maximum.
Since the coefficient of the x² term is positive, the second derivative will be positive, confirming the presence of a minimum.