1. Find the derivative of the function y (x). y ‘(x) = 1/2 + 3x ^ 2.
2. Let us examine the function y ‘(x). y ‘(x) = 1/2 + 3x ^ 2. The first term is greater than zero, the second term is greater than or equal to zero. y ‘(x) = 1/2 + 3x ^ 2> 0 for any value of x.
3. The function y (x) increases over the entire numerical interval, there are no extreme points.
4. y (0) = 0 is the smallest value of the function y (3) = 3/2 + 27 = 28.5 is the largest value of the function.
Answer. On the segment [0; 3], the smallest value of the function is 0, the largest value of the function is 28.5.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.