If fx-0 for x-0 and fx is differentiable at x-0- then for x- 0- fx may be

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Higher Order Derivatives

If fx=0 for...

Question

If $f (x) = 0$ for $x < 0$ and $f (x)$ is differentiable at $x = 0$ , then for $x \geq 0, f (x)$ may be

x^{2}

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x

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- x

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- x^{3 / 2}

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$If f (x) = (\begin{matrix} x^{3} + x^{2}, f o r 0 \leq x \leq 2 x + 2, f o r 2 \leq x \leq 4 \end{matrix}$
then the odd extension of f(x) would be -

f (x) = x

x \in Q, f (x) = x^{2} + x

x

f

x = 0

f^{'} (0) = 1

If f(x) = $x^{3} + x^{2}$ for 0 $\leq x \leq 2$ then the odd extension of f(x) would be -

x +2 for 2 < x $\leq$ 4

f (x) = a | sin x | + b e^{| x |} + c | x^{3} |

x = 0

∣ ∣ x^{3} ∣ ∣

x = 0

x = a

| f (x) |

x = a

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