How to find (f) if f′(x)=16x^3+6x+7 and f(1)=−1 ?
3 Answers
Explanation:
We start by integrating both sides.
f(x) = int 16x^3 + 6x + 7 dxf(x)=∫16x3+6x+7dx
f(x) = 4x^4 + 3x^2 + 7x + Cf(x)=4x4+3x2+7x+C
Now we solve for
-1 = 4(1)^4 + 3(1)^2 + 7(1) + C−1=4(1)4+3(1)2+7(1)+C
-1 = 4 + 3 + 7 + C−1=4+3+7+C
-1 - 14 = C−1−14=C
C = -15C=−15
Hopefully this helps!
Explanation:
Integrate:
So
Plug in
Set
Solve for C:
So your
Explanation:
We got:
And so,
Therefore,
So, the original function