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Question

f(x) = sinx is decreasing about x=π.


A

True

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B

False

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Solution

The correct option is B

True


As we saw, a function is decreasing at a point x = a, if it is decreasing in the neighborhood. So, we will find the value of the function at x = a-h, a and a+h. If we get a relation

f(a-h) f(a) f(a+h), then we say that the function is decreasing at x = a. This could be lengthy.

Instead, if we have f’(a) 0, we can say that the function is decreasing about x =a.

So, we will find f’( π ) to check if the function is decreasing about x = π

f’(x) = cos(x)

f’( π ) = cos ( π ) = -1

Which is negative. So we can clearly say that the function is decreasing about x = π.


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