Question

Write two different explanations of the relationship between the expressions 4x^3 and x^4, one using the word derivative and the other using the word antiderivative. Then give an example of a pair of expressions that have the same relationship. If necessary, use the carat ^ for powers, such as x^5 for "x to the fifth power" or x^3 for "x to the third power."

Answer 1

If f(x) = x^4, then derivative f'(x) = 4 x^3
If you integrate 4x^3 , integral F(x) = x^4 + C
C in an integration constant.