How to find (f) if f′(x)=16x^3+6x+7 and f(1)=−1 ?

Draven Crane

Draven Crane

Answered question

2022-12-21

How to find (f) if f(x)=16x3+6x+7 and f(1)=−1 ?

Answer & Explanation

Alleryexerimivn3

Alleryexerimivn3

Beginner2022-12-22Added 8 answers

Integrating both sides comes first.
f(x)=16x3+6x+7dx
f(x)=4x4+3x2+7x+C
We now determine C.
1=4(1)4+3(1)2+7(1)+C
1=4+3+7+C
114=C
C=15
oppsiktrl3

oppsiktrl3

Beginner2022-12-23Added 2 answers

Integrate:
16x3 becomes 4x4
6x becomes 3x2
7 becomes 7x
So f(x) is 4x4+3x2+7x+C.
Plug in x=1:
4(14)+3(12)+7(1)+C
=4+3+7+C
=14+C
Set 14+C equal to -1:
1=14+C
Then we need solving for C:
15=C
So your f(x)=4x4+3x2+7x15

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