If f(x) = sin(x) + cos(x), then the critical points in the interval [0, 2π] are:

Practice Questions

1 question

π/4, 5π/4
π/2, 3π/2
0, π
π/3, 2π/3

Questions & Step-by-step Solutions

1 item

Q: If f(x) = sin(x) + cos(x), then the critical points in the interval [0, 2π] are:

Solution: To find critical points, we set f'(x) = cos(x) - sin(x) = 0. This gives tan(x) = 1, leading to x = π/4 and x = 5π/4 in the interval [0, 2π].

Steps: 7

Step 1: Identify the function f(x) = sin(x) + cos(x).
Step 2: Find the derivative of the function, f'(x). The derivative is f'(x) = cos(x) - sin(x).
Step 3: Set the derivative equal to zero to find critical points: cos(x) - sin(x) = 0.
Step 4: Rearrange the equation to get cos(x) = sin(x).
Step 5: Divide both sides by cos(x) (assuming cos(x) is not zero) to get tan(x) = 1.
Step 6: Find the angles where tan(x) = 1. These angles are x = π/4 and x = 5π/4.
Step 7: Check if these angles are within the interval [0, 2π]. Both π/4 and 5π/4 are in this interval.

If f(x) = sin(x) + cos(x), then the critical points in the interval [0, 2π] are:

Practice Questions

Questions & Step-by-step Solutions

Related Questions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?