Math Problem Statement
f(x) = 5 sin(x) + 5 cos(x), 0 ≤ x ≤ 2𝜋, find the interval on which f is concave down and up
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Calculus
Concavity
Second Derivative Test
Trigonometric Identities
Formulas
f(x) = 5sin(x) + 5cos(x)
Trigonometric identity: sin(x) + cos(x) = √2 sin(x + π/4)
Second derivative f''(x) to determine concavity
Theorems
Second Derivative Test
Suitable Grade Level
Grades 11-12
Related Recommendation
Determine Concavity of Sinusoidal Functions on an Interval
Analyze the Function f(x) = x - 2 sin(x): Intervals of Increase, Decrease, and Relative Extrema
Find the Absolute Maximum of f(x) on the Interval [-4, 2]
Find Local Maxima and Minima of f(x) = sin(2x) - x using the First Derivative Test
Determine Increasing and Decreasing Intervals for f(x) = -3cos²(x) - 3cos(2x)