Answer:
To determine the consecutive integer values of x between which the real zero is located, you can use the Rational Root Theorem. The Rational Root Theorem states that, if the polynomial equation ax^n + bx^n-1 + cx^n-2...+ z = 0 has integer coefficients, then the possible rational roots of the equation are the factors of z divided by the factors of a. In this case, z = -4 and a = 1, so the possible rational roots of the equation are ±1, ±2, and ±4. Therefore, the consecutive integer values of x between which the real zero is located are -4 and -2.
To estimate the x-coordinate at which the minima and maxima occur for the given function, you can use calculus. Taking the first derivative of the function and setting it equal to 0 will allow you to determine the x-coordinate at which the minima and maxima occur. Doing so, you get 3x^2 + 12x + 6 = 0, and solving for x, you get x = -2 or x = -1. Therefore, the x-coordinate at which the minima and maxima occur is approximately -2 and -1.