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:

  1. 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.



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