SATHEE: Application of Derivatives 3 Question 2

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 $[t, t + π]$ , such that $f^{'} (c) = 0$ .

Because

Statement II $f (t) = f (t + 2 π)$ 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

(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 $f^{'} (c) = 0$

Hence, Statement I is true.

Statement II $f (t) = f (t + 2 π)$ is true. But statement II is not correct explanation for statement I.

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Application of Derivatives 3 Question 2

2. Let f(x)=2+cos⁡x, for all real x.

Analytical & Descriptive Question

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2. Let $f (x) = 2 + \cos x$ , for all real $x$ .