The smallest and largest value of the function y = 3x ^ 2, on the half-interval (0; 4)

Find the derivative of the function y = 3x squared, we get: 6x. Equate the derivative to zero and solve the equation 6x = 0; x = 0 coincides with the beginning of this interval (0; 4]. Then we find the value of the function at the ends of the interval y (0) = 3 (0) squared = 3 * 0 = 0 and y (3) = 3 * (3) in squared = 3 * 3 * 3 = 27. The largest value of the function y (3) = 27, the smallest value of the function y (0) = 0.