Question

Integration. The derivative of the function f is given by f^1(x) = 4x^5+8x. The graph of f passes through the point (0,8). Find the expression for f(x)

Answer 1

anti derivative is the opposite of derivative

for term 8x, what term would be 8x if derived?
deriving reduces the exponent, so it should be x^2

deriving x^2 doubles the number, so we should have a half of it:
4x^2 should get 8x if derived

Answer 2

The anti derivative of the equation given would be x^6+x^2+ c...then what?

Answer 3

I'm supposed to be finding an expression for f(x) in terms of the equation given f^1(x) = 4x^5+8x

Answer 4

yes, you have a +c in there. a normal function f(x) should not have UNKNOWN CONSTANTS.

you use the additional information to determine what the constant should be
this is necessary because constants are not carried into a derivative of the function, so the value of the constant was lost and missing in f^1