Question #d7d5a

1 Answer
Dec 10, 2016

a=3 and f(x)=x^4

Explanation:

The definition of the derivative of y=f(x) is

f'(x)=lim_(h rarr 0) ( f(x+h)-f(x) ) / h

Compare this derivative definition with the given limit:

f'(a) = lim_(h rarr 0) ( (3+h)^4-81 ) / h = lim_(h rarr 0) ( (3+h)^4-3^4 ) / h

And we see that a=3 and that f(x)=x^4