JEE MAIN - Mathematics (2021 - 26th August Evening Shift - No. 1)
Let [t] denote the greatest integer less than or equal to t. Let
f(x) = x $$-$$ [x], g(x) = 1 $$-$$ x + [x], and h(x) = min{f(x), g(x)}, x $$\in$$ [$$-$$2, 2]. Then h is :
f(x) = x $$-$$ [x], g(x) = 1 $$-$$ x + [x], and h(x) = min{f(x), g(x)}, x $$\in$$ [$$-$$2, 2]. Then h is :
continuous in [$$-$$2, 2] but not differentiable at more than
four points in ($$-$$2, 2)
four points in ($$-$$2, 2)
not continuous at exactly three points in [$$-$$2, 2]
continuous in [$$-$$2, 2] but not differentiable at exactly
three points in ($$-$$2, 2)
three points in ($$-$$2, 2)
not continuous at exactly four points in [$$-$$2, 2]
Explanation
min{x $$-$$ [x], 1 $$-$$ x + [x]}
h(x) = min{x $$-$$ [x], 1 $$-$$ [x $$-$$ [x])}
_26th_August_Evening_Shift_en_1_2.png)
$$\Rightarrow$$ always continuous in [$$-$$2, 2] but not differentiable at 7 points.
h(x) = min{x $$-$$ [x], 1 $$-$$ [x $$-$$ [x])}
$$\Rightarrow$$ always continuous in [$$-$$2, 2] but not differentiable at 7 points.
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