Consider the function

Question

I've been trying to figure out this problem for some time now.

Consider the function f(x)=x⁴+7√(x).

Let F(x) be the antiderivative of f(x) with F(1)=-5

Then F(x) =_______________

I found the antiderivative of f(x)

((14x^3/2)/3)+(x⁵/5)+C

Then I tried substituting -5 for x and this is what I got, but it said that it won't accept the answer because:

(14(-5)^(3/2))/3-625

"Can't raise a negative number to a non-integer power"

And I tried substituting -5 for C, but that was also incorrect.

I don't get what it is asking. Many thanks to you if you can help!

Answer 1

You're almost there!

Recall that the function is F(x). So if F(1) = -5, we need to plug in 1 for x.

((14x^3/2)/3)+(x⁵/5)+C

((14*(1)^3/2)/3)+((1)⁵/5)+C = -5

14/3 + 1/5 + C = -5

70/15 + 3/15 + C = -5

73/15 + C = -75/15

C = -148/15

F(x) = ((14x^3/2)/3)+(x⁵/5)-148/15

Answer 2

The function f(x) has domain all nonnegative numbers (and the same is true for F(x)) since you have a square root of x in one of the expressions. This means that you are not allowed to plug in the number -5 as you did. Actually, it says F(1)=-5 and not F(-5)=something. So you don't really have to put x=-5.