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f(x)=x23x+9 then the derivative of  f(x) in the interval  (0,5) is

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a
0
b
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c
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d
Does not exist

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detailed solution

Correct option is D

f(x)=x23x+9

=(x3)2

f(x)=|x3|

f(x)={x3,x33x,x<3

f|(x)={1,ifx31,ifx<3

f(x) is differentiable at all points on the interval (0,5) except at  x=3

 the derivative of f(x) on the interval (0,5) does not exist. 

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