If $$f(x)=a$$|$$sin$$⁡x|$$+be$$|x|$$+c$$|x|$$3$$ and if $$f(x)$$ is differentiable at $$x=0$$, then

Question

If $$f(x)=a$$|$$sin$$⁡x|$$+be$$|x|$$+c$$|x|$$3$$ and if $$f(x)$$ is differentiable  at $$x=0$$, then

Infinity Learn · Accepted Answer

If  x≥$$0$$  then  $$fx=a$$ $$sin$$ x $$+$$ b ex $$+$$ c $$x3$$                           f'(x)=a$$ $$cos$$ x $$+$$ b ex $$+$$ c $$3x2$$  f'$$0+=$$ a $$+$$ b $$+$$ $$0$$ $$=$$ a $$+$$ b If  x<$$0$$  then fx $$=$$ $$-a$$ sinx $$+$$ b $$e-x-c$$ $$x3$$                          f'x $$=-a$$ $$cos$$ x $$-$$ b $$e-x$$ $$-3cx2$$                         f' $$0-=$$ $$-a$$ $$-b$$    since f is differentiable at x $$=$$ $$0$$ ,           f'$$0+$$ $$=f$$'$$0-$$ ⇒ $$a+b$$ $$=$$ $$-a-b$$ ⇒ a $$+$$ b $$=$$ $$0$$    and  c ∈ R        so option is  $$(2)

$If f (x) = a | \sin x | + b e^{| x |} + c | x |^{3} and if f (x) is differentiable at x = 0, then$

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If f(x)=a|sin⁡x|+be|x|+c|x|3 and if f(x) is differentiable at x=0, then

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$If f (x) = a | \sin x | + b e^{| x |} + c | x |^{3} and if f (x) is differentiable at x = 0, then$