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Expansion of (x+a)(x+b)

Let f(x)=ax^2...

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{ Let }f(x)=ax^2-b\vert x\vert, where }a and }b are constant. }}{ Then at }x=0,f(x) has

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f (x) = a x^{2} - b | x |

a

b

are constants. Then at

x = 0, f (x)

f (x) = a x^{2} - b | x |,

where a and b are constants. Then at x = 0, f(x) is

f (x) = a + b | x | + c {| x |}^{4}

a, b

c

are real constants. Then

f (x)

is differentiable at

x = 0

f (x) = {\begin{matrix} \begin{matrix} x g (x), & x \leq 0 \end{matrix} \begin{matrix} x + a x^{2} - x^{3}, & x > 0 \end{matrix} \end{matrix}

g (t) = {lim}_{x \to 0} {(1 + a tan x)}^{t / x}

a

is positive constant, then

f (x)

is differentiable at

x = 0

a \in

f (x) = a x^{2} - b x + c^{2}, b \neq 0

f (x) \neq 0

x \in R

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