1. ## integration help

help pls

a) if d^2y/d^2x = 6x+4 and dy/dx=8 and y=2 when x=1, find your site a function of x

b) if f''(x)=x, f'(2)=1 and f (3)=0, find f (x)

c) if f''(x) =-2x and the curve y=f (x) has a stationary point at (2,6), find the equation of this curve

thank uu

2. ## Re: integration help

Could you clarify the meaning of ‘the site of function of x’, for ‘a)’ ?

3. ## Re: integration help

oh sorry - I meant "find y as a function of x"

4. ## Re: integration help

For a)
d^2y/d^2x = 6x+4
dy/dx = 3x^2+4x+c1
Since dy/dx=8 when x=1
8 = 3(1)^2+4(1)+c1
c1 = -5
dy/dx = 3x^2+4x-5
y = x^3+2x^2-5x+c2
Since y=2 when x=1
2 = (1)^3+2(1)^2-5(1)+c2
c2 = 4
Therefore y = x^3+2x^2-5x+4

5. ## Re: integration help

For b)
f''(x)=x
f'(x)=x^2/2+c1
Since f'(2)=1
1=(2)^2/2+c1
c1=-1
f'(x)=x^2/2-1
f(x)=x^3/6-x+c2
Since f(3)=0
0=(3)^3/6-(3)+c2
c2=-3/2
Therefore f(x)=x^3/6-x-3/2

6. ## Re: integration help

thank you for the help!! <3

7. ## Re: integration help

Generally with these types of questions you should write out the primitive function including any unknown constants, then use the points that are given to you to figure out what the constants are.

8. ## Re: integration help

Also "has a stationary point at (2,6)" implies that at x=2, y'=0 and at x=2, y=6

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