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Answer :
The function f(x) = x3 - 6x2 - 36x + 72 reaches a maximum at f(maximum) = 150 and a minimum at f(minimum) = 42. These values are obtained by finding the derivative of the function, setting it equal to zero to get the critical points, and then substituting those points back into the original function. The correct option is d.
The function given is a cubic function, f(x) = x3 - 6x2 - 36x + 72. To find the maximum or minimum values of this function, you would first need to find its derivative, which is f'(x) = 3x2 - 12x - 36. Setting this equal to zero gives us the critical points of the function.
Solving this equation for x gives x = -3 and x = 4. By plugging these values back into the original function, you can find that f(-3) = 150 (maximum) and f(4) = 42 (minimum).
So the maximum and minimum values of the function are f(maximum) = 150 and f(minimum) = 42. Option d is the correct answer.
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