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

June 29, 2021 | education

| 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.