Final answer:
The function f(x) = 2x^2 - 10x - 30 is concave upward.
Step-by-step explanation:
The concavity of a function can be determined by examining the second derivative of the function. If the second derivative is positive, the function is concave upward, and if the second derivative is negative, the function is concave downward. If the second derivative is zero, the function may have a point of inflection where the concavity changes.
To find the second derivative of the function f(x) = 2x^2 - 10x - 30, first differentiate the function to get f'(x) = 4x - 10. Then differentiate again to get f''(x) = 4. Since the second derivative is positive (4), the function is concave upward throughout. It does not have any points of inflection.