Find the largest value of the function y = x ^ -4 in the interval (-3; -1].

1. Find the domain of the function:

y = x ^ (- 4);
x ≠ 0;
x ∈ (-∞; 0) ∪ (0; ∞).
2. We calculate the first derivative of the function and find its critical points:

y = 1 / x ^ 4;
y ‘= -4 * x ^ (- 5);
y ‘= -4 / x ^ 5;
-4 / x ^ 5 = 0.
The equation has no solutions, therefore, the function has no critical points.

3. Determine the values of the function at the ends of the given half-interval (-3; -1]:

y = 1 / x ^ 4;
y (-3) = 1/3 ^ 4 = 1/81;
y (-1) = 1/1 ^ 4 = 1.
y (max) = 1.
Answer. The largest value of the function y = x ^ (- 4) in the interval (-3; -1]: 1.