integration qn (1 Viewer)

[bos1234]

A curve with gradient function f'(x) = cx + d has a turning pt at (2,0) and crosses the y-axis when y=4. Find c and d, and hence find the eqn of the curve.

---------------------------------------------------------------------------------
at turning pt f'(x)=0

0=2c + d
c= -d/2

f(x) = cx^2 + dx + 4
........---
.........2


what do i do after these steps?.. ignore the full stops

 

[pLuvia]

Now since you know there is a turning point at (2,0) substitute that into your new found equation. Then you have an equation in c and d. Substitute your
c=-d/2 into the new equation and you can solve for c and d

 

[bos1234]

r u subbing in 2,0 because if its a turning pt then f(x) has a root at 2?

 

[blackfriday]

uh huh...

 

[jyu]

A curve with gradient function f'(x) = cx + d has a turning pt at (2,0) and crosses the y-axis when y=4. Find c and d, and hence find the eqn of the curve.

---------------------------------------------------------------------------------
at turning pt f'(x)=0

0=2c + d
c= -d/2

f(x) = cx^2 + dx + 4
........---
.........2


what do i do after these steps?.. ignore the full stops

f'(x) = cx + d implies that f(x) is quadratic.

Turning pt at (2,0) gives f(x) = a(x-2)^2.

Crosses the y-axis when y=4: 4 = a(0-2)^2, therefore a = 1.

Hence f(x) =(x-2)^2, and f'(x) =2x-4.

c = 2 and d = -4.