Application of Derivatives 3 Question 2
2. Let $f(x)=2+\cos x$, for all real $x$.
Statement I For each real $t$, there exists a point $c$ in $[t, t+\pi]$, such that $f^{\prime}(c)=0$.
Because
Statement II $f(t)=f(t+2 \pi)$ for each real $t$. (2007, 3M)
(a) Statement I is correct, Statement II is also correct; Statement II is the correct explanation of Statement I
(b) Statement I is correct, Statement II is also correct; Statement II is not the correct explanation of Statement I
(c) Statement I is correct; Statement II is incorrect
(d) Statement I is incorrect; Statement II is correct
Analytical & Descriptive Question
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Answer:
Correct Answer: 2. (b)
Solution:
- Given, $f(x)=2+\cos x, \forall x \in R$
Statement I There exists a point $\in[t, t+r]$, where $f^{\prime}(c)=0$
Hence, Statement I is true.
Statement II $f(t)=f(t+2 \pi)$ is true. But statement II is not correct explanation for statement I.
