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  • Consider the function <img alt="f(x)=\left | x-2 \right |+\left | x-5 \right |,x\; \epsilon \, R." src="https://entrancecorner.oncodecogs.com/gif.latex?f%28x%29%3D%5Cleft%20%7C%20x-2%20%5Cright%20%

Consider the function f(x)=\left | x-2 \right |+\left | x-5 \right |,x\; \epsilon \, R.

Statement 1: f'(4)=0  

Statement 2: f is continuous in \left [ 2,5 \right ] , differentiable in (2,5) and f(2)=f(5).

 

 

Option: 1

Statement 1 is false, statement 2 is true


Option: 2

Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1


Option: 3

Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1


Option: 4

Statement 1 is true, statement 2 is false


Answers (1)

best_answer

f(x)=\left | x-2 \right |+\left | x-5 \right |

\\\\f(x)=3,\:\:2\leq x\leq 5\\f'(x)=0\\f'(4)=0\\

Statement-1 :\; f'(4)=0.\; True

Statement-2 :\; f\; is \; continuous\; in\; \left [ 2,5 \right ], differentiable\; in\; \left ( 2,5 \right )\; and\; f(2)=f(5).\; True

But \; Statement \; 2 \; is \; not\; a \; correct\; explanation \; for\: \; statement \; 1.

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Deependra Verma

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