Question
Find the value of c which satisfies Rolle's Theorem for the function
f(x)=sin(x^2)on (0, ãpi).
f(x)=sin(x^2)on (0, ãpi).
Answers
Steve
f(0) = 0
f(√π) = 0
So, we need c in (0,π) such that f'(c) = 0
f'(x) = 2x cos(x^2)
2x cos(x^2) = 0
Clearly c=√(π/2) satisfies the theorem.
f(√π) = 0
So, we need c in (0,π) such that f'(c) = 0
f'(x) = 2x cos(x^2)
2x cos(x^2) = 0
Clearly c=√(π/2) satisfies the theorem.