Solve the differential equation

Question

asked Sep 20, 2022 78.8k views

1 Answer

Anthony Calandra · Answer 1 · 2022-09-27T01:30:00+0000

Answer:

f(x) = 3x^2+8

Explanation:

We are given the first derivative of
f(x) and the value of
f(0) .

To go from the first derivative to the original function, we integrate.

Therefore:

$f(x) = \int {6x} \, dx$

To integrate, we add 1 to the power and divide by the new power:

$\int {6x} \, dx = (6x^2)/(2) =3x^2+C$

Because we have an indefinite integral, we have to add the constant,
, to the end.

So:
f(x) = 3x^2+C

We know
f(0) so we can find the constant
.

f(0)=3(0)^2+C=8

C=8

Therefore
f(x) = 3x^2+8