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# Differentiation and integration watch

1. the diagram shows a part of the graphy of
y=x-2x^4

ai) find f'(x)
aii ) show that the x coordinate of the stationery point P is 1/2
aiii) find the y-coordinate of P

bi) find |(x-2x^4)dx
bii) hence find the area of the shaded region

ive worked out ai and bi, but idk how to do aii and aiii
2. (Original post by Chez 01)
the diagram shows a part of the graphy of
y=x-2x^4

ai) find f'(x)
aii ) show that the x coordinate of the stationery point P is 1/2
aiii) find the y-coordinate of P

bi) find |(x-2x^4)dx
bii) hence find the area of the shaded region

ive worked out ai and bi, but idk how to do aii and aiii
aii - Stationary points are those where , so you solve this equation and show that

aiii - You then know the x-coordinate of the stationary point, so just find its y-coordinate by using
3. If you’ve done ai) then you’ve differentiated - for aii) make your differential equal 0 and solve to hopefully get x = 1/2. For aiii) just sub in x = 1/2 to the original equation. For bii) integrate between the two x values of the shaded region, provided the region is positive - if it does cross the x-axis, integrate the parts above and below the axis separately and add the modulus of both answers together to get total area. Hope that helps
4. (Original post by Rocco123)
If you’ve done ai) then you’ve differentiated - for aii) make your differential equal 0 and solve to hopefully get x = 1/2. For aiii) just sub in x = 1/2 to the original equation. For bii) integrate between the two x values of the shaded region, provided the region is positive - if it does cross the x-axis, integrate the parts above and below the axis separately and add the modulus of both answers together to get total area. Hope that helps

thankyouu for explaining it clearly, ive worked out the answers to aii and aiii, but im still not sure about bii, i dnt understand how to work out the x values of the shaded region
5. (Original post by Chez 01)
thankyouu for explaining it clearly, ive worked out the answers to aii and aiii, but im still not sure about bii, i dnt understand how to work out the x values of the shaded region
Could you put a picture of the graph up?
6. (Original post by RDKGames)
aii - Stationary points are those where , so you solve this equation and show that

aiii - You then know the x-coordinate of the stationary point, so just find its y-coordinate by using
7. (Original post by Chez 01)
the diagram shows a part of the graphy of
y=x-2x^4

ai) find f'(x)
aii ) show that the x coordinate of the stationery point P is 1/2
aiii) find the y-coordinate of P

bi) find |(x-2x^4)dx
bii) hence find the area of the shaded region

ive worked out ai and bi, but idk how to do aii and aiii
If P is a stationary point, then the f'(x) = 0 at that point, so solve for that value. Plug in to the original function to then get the y-coordinate of P at that point. For part bii, I can't help because the diagram won't load, sorry!
8. (Original post by Rocco123)
Could you put a picture of the graph up?
https://imgur.com/a/MwFgr
9. The area shaded is equivalent to . You do most of this work in part bi, so now just use it and apply the limits.
10. (Original post by RDKGames)
The area shaded is equivalent to . You do most of this work in part bi, so now just use it and apply the limits.
how did u work out the limits

thankyou too
11. (Original post by Chez 01)
how did u work out the limits

thankyou too
oh nevermind, i understand

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