Differentiation

Edexcel IAL WMA12/01 /P2/June 2022/Q8 (Differentiation Stationary Points)

In this question you must show all stages of your working.

Solutions relying entirely on calculator technology are not acceptable.

A curve has equation​​ 

y = 256x4 - 304x - 35 +27x2        x ≠ 0

• Find​​ dydx​​ 

(3)

• Hence find the coordinates of the stationary points of the curve.​​ 

(5)

SOLUTION​​ 

a-​​ Differentiating once the equation of​​ y.​​ 

y=256x4-304x1-35+27x-2

dydx=1024 x3-304-54x-3

b-​​ 

Since at the stationary points the of curve the gradient is zero, therefore​​ dydx=0. Hence, equating the diffrentiated expression to zero to find the value of x and at last substituting the calculated value of x in the parent equation or the equation of the curve to find the y-coirdinate of the stationary point.​​ 

dydx=0

1024 x3-304-54x-3=0

1024 x3-304-54x3=0

1024x6-304x3-54=0

Let​​ u=x3, then the equation would be​​ 

1024 u2-304 u-54=0

512u2-152u-27=0

u=--152±-1522-4512-272512

u=2764               u=-18

Since​​ u=x3, so​​ 

x3=2764               x3=-18

x=34                 x=-12

So when​​ x=34,  

y=256344-30434-35+27342

y= -134

And, when​​ x=-12 

 y=256-124-304-12 -35+27-122

y=241

Hence, the coordinates of stationary points are​​ 34  , -134  & -12,      241