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Let f be a function with continuous seco...

Let `f` be a function with continuous second derivative and `f(0)=f^(prime)(0)=0.` Determine a function `g` by `g(x)={(f(x))/x ,x!=0; 0,x=0` Then which of the following statements is correct?
a. `g` has a continuous first derivative b. `g` has a first derivative c. `g` is continuous but `g` fails to have a derivative d. `g` has a first derivative but the first derivative is not continuous

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