Final answer:
To find the relative extrema of the function f(x) = -12x² - 2x - 10, take the derivative, set it equal to zero, and find the x-value. Plug that value back into the original function to get the y-value. The relative minimum is (-1/12, -35/12).
Step-by-step explanation:
To find the relative extrema of the function f(x) = -12x² - 2x - 10, we need to take the derivative of the function and set it equal to zero. The derivative of f(x) is f'(x) = -24x - 2. Setting f'(x) = 0, we get -24x - 2 = 0. Solving for x, we find that x = -1/12. Plugging this value back into the original function, we find that f(-1/12) = -35/12.
Therefore, the relative minimum of the function f(x) = -12x² - 2x - 10 is (-1/12, -35/12).