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The derivative of a function f with respect to x is given by...

The derivative of a function f with respect to x is given by f(x)=3x24x5. If f(1)=4, find f(x).

A.

f(x)=x31x4+2

B.

f(x)=x3+1x4+2

C.

f(x)=x31x42

D.

f(x)=x3+1x42

Correct answer is B

dydx=3x24x5=3x24x5

y=(3x24x5)dx

y=x3+1x4+c

f(1) = 4; 4=13+114+c4=2+c

c=2

f(x)=x3+1x4+2