If a function f is continuous on a closed interval [a, b], then f has an absolute max and an absolute min on the interval. Each of these occur at either an endpoint of the interval or at a critical number of f. This is by virtue of the Extreme Value Theorem.
f'(x) = 0 - 14x = -14x
f'(x) = -14x = 0
x = 0, so this is a critical number of f
f(0) = 5 - 7(0) = 5 - 0 = 5
Now, let's check the endpoints of the closed interval
f(-3) = 5 - 7(-3)² = 5 - 7(9) = 5 - 63 = -58
f(1) = 5 - 7(1)² = 5 - 7 = -2
Absolute max value is 5, and it occurs at x = 0
Absolute min value is -58, and it occurs at x = -3
