Primitive function (1 Viewer)

[mtsmahia]

Q) A Curve has y double dash= 8x and the tangent at (-2,5) makes an angle of 45* with the x-axis. Find the equation of the curve ?

Thanks

 

[Trebla]

Q) A Curve has y double dash= 8x and the tangent at (-2,5) makes an angle of 45* with the x-axis. Find the equation of the curve ?

Thanks

y'' = 8x
y' = 4x² + c
If it makes an angle of 45 degrees with the x-axis then the gradient is 1 at (-2, 5)
4(-2)² + c₁ = 1
c₁ = - 15
Thus
y' = 4x² - 15
y = 4x³/3 - 15x + c₂
Sub (-2, 5) since it lies on the curve
5 = - 32/3 - 15(-2) + c₂
c₂ = - 43/3
Hence
y = 4x³/3 - 15x - 43/3

Check my working...hope that's right...

 

[mtsmahia]

y'' = 8x
y' = 4x² + c
If it makes an angle of 45 degrees with the x-axis then the gradient is 1 at (-2, 5)
4(-2)² + c₁ = 1
c₁ = - 15
Thus
y' = 4x² - 15
y = 4x³/3 - 15x + c₂
Sub (-2, 5) since it lies on the curve
5 = - 32/3 - 15(-2) + c₂
c₂ = - 43/3
Hence
y = 4x³/3 - 15x - 43/3

Check my working...hope that's right...

yep! its right , thanks