According to the Mean Value theorem conditions. The answer will be (a) that is Mean Value Theorem can be applied.
The Mean Value Theorem says that there exists a point c in the interval (a, b) such that f'(c) equals the function's average rate of change throughout [a , b] if a function f is continuous on the closed interval [a , b] and differentiable on the open interval (a , b).
The name derives from the fact that an average rate of change during an interval may be considered as an average (or mean) of the instantaneous rates of change along the interval thanks to the fundamental theorem of calculus.
[tex]f(x) = 9\sin x[/tex] is continuous on [0,1] since every value for [tex]9\sin x[/tex] exist in that interval.
[tex]f(x) = 9\sin x[/tex] is differentiable on (0,1) since at every point the derivative exist that is [tex]9 \cos x[/tex] is valid in that interval.
The answer is (a) that is Yes, The Mean Value Theorem can be applied.
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