The function defined by fx-max -x2-x-12- 2 x1-x- 0 - x - 1

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Geometrical Explanation of Rolle's Theorem

The function ...

Question

The function defined by f(x) = $m a x . {x^{2}, (x - 1)^{2}, 2 x (1 - x), 0 \leq x \leq 1}$

is differentiable for all x

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is differentiable for all x except at one point

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is differentiable for all x except at two point

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is not differentiable at more than two point

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Solution

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Similar questions

f (x) = max {x^{2}, (x - 1)^{2}, 2 x (1 - x)}

0 < x < 1

f (x) = \frac{x}{1 + x}

[0, \infty) \to [0, \infty), f (x)

f

f (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} 1 - x, & x < 0 1, & x = 0 x + 1, & x > 0 \end{matrix}

f (x)

f (x)

f (x) = \frac{sin x}{x} + cos x x > 0

= 2 x = 0

= \frac{4 (1 - \sqrt{1 - x})}{x} x < 0

x = 0

f

f (x) = \frac{1}{x}, x \neq 0

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