find y=f(x) if fsecond derivitive of x=x+2 f first derivitive of 0=3 f(0)=-1?

Answer 1

f''(x) = x+2

Integrate this to obtain f'(x)
f'(x) = S(x+2)dx
f'(x) = (x^2)/2 + 2x + C

Now solve to find the value of C.
If f'(0) = 3
3 = (0^2) + 2(0) + C
C = 3
Therefore, f'(x) = (x^2)/2 + 2x + 3

Now integrate this to obtain f(x)
f(x) = S((x^2)/2 + 2x + 3)dx
f(x) = (x^3)/6 + x^2 + 3x + C

Now solve to find the value of C
If f(0) = -1
-1 = (0^3)/6 + (0)^2 + 3(0) + C
C = -1

Therefore,
f(x) = (x^3)/6 + x^2 + 3x - 1 is your answer

PS. Puggy's answer is incorrect, that is the value of the first derivative. Forgot to do it twice.

Answer 2

Find y=f(x) if the second derivative of f(x) =x+2 and the first derivative = 0 when x=3. Also f(0) = -1?

I appologize, but this was the only way your question made sense to me.

y" = x+2
y' = x^2/2 + 2x +c
Since 1st derivative 3 when x = 0 , we get:
0 = 3^2/2 + 2*3 + c
c = -9/2 - 6 = -21/2
so y' = x^2/2 +2x -21/2
y = f(x) = (x^3)/6 + 2x^2 -(21/2)x + k
Since f(0) = -1, we get -1 = k
So f(x) = (x^3)/6 + 2x^2 - (21/2)x -1

Answer 3

It is given that

f'(x) = x + 2

Therefore, using the reverse power rule,

f(x) = (1/2)x^2 + 2x + C

But f(0) = -1, therefore

f(0) = (1/2)(0)^2 + 2(0) + c
-1 = C

Therefore

f(x) = (1/2)x^2 + 2x - 1

(p.s. your question is not 100% clear)

Answer 4

Please restate your question. Make sure that you are clear in explaining what you need to do. Use proper shorthand and notation. For example, if you are saying that the value of the first derivative evaluated at 3 is equal to 0, then write f '(3) = 0.

Answer 5

You need to resubmit this problem after you have cleaned it up. It's full of typos and crap to the point that it's not clear what you are asking for.