Find the critical points of the function y = x-cos x.
May 30, 2021 | education
| 1. Let’s calculate the derivative of the function:
y (x) = x – cosx;
y ‘(x) = 1 + sinx.
2. The derivative of a continuous and smooth function at critical points is equal to zero:
y ‘(x) = 0;
1 + sinx = 0;
sinx = -1;
x = -π / 2 + 2πk, k ∈ Z.
3. On the entire set of real numbers, the derivative of the function is greater than or equal to zero:
sinx ≥ -1;
sinx + 1 ≥ 0;
y ‘(x) ≥ 0,
hence, the function increases and the critical points are not extremum points.
Answer: critical points of the function: -π / 2 + 2πk, k ∈ Z.
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