Let’s find the first derivative of this function:
y ’(x) = (3 * x + 5)’ = 3.
Equating the derivative to zero:
3 ≠ 0, therefore, there are no global extrema.
Let’s calculate the value of the function at the ends of the segment, that is, for x = -5, x = 7:
y (-5) = 3 * (-5) + 5 = -15 + 5 = -10.
y (7) = 3 * 7 + 5 = 26.
Answer: the largest value of the function ymax = 26, the smallest value of the function ymin = -10.
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