WMA11 October 2022

1.​​ WMA11/01​​ Edexcel​​ IAL P1 October 2022, Q1​​ (Differentiation:​​ Equations of Tangents)

The curve C has equation​​ 

y=x34-x2+17x      x>0

(a) Find​​ dydx, giving your answer in simplest form.​​ 

(3)

The point​​ R2,132​​ lies on C.​​ 

(b) Find the equation of the tangent to C at the point R.​​ 

Write your answer in the form ax + by + c = 0, where a, b and c are integers to be found.​​ 

(3)

SOLUTION

a-​​ Differentiating the given function expression.​​ 

y=14x3-x2+17x-1

dydx=34x2-2x1-17x-2

dydx=34x2-2x-17x2

b-​​ 

We need to find the equation of a line of tangent to curve at point R. For that, we need the slope of tangential line and then use the point slope formula to get the equation of tangential line.​​ 

Putting the x-coordinate of point R (2,132) in the equation of tangent to curve C to find the gradient of the tangential line.

dydx=mT=34x2-2x-17x2

mT=3422-22-1722

mT=344-4-174

mT=-1-174

mT=-214

Now, substtituting the x and y coordinate in the point-slope formula to find the equation of tangential line.

y-y1=mx-x1

y-132=-214x-2

4y-132=4 x -214 x-2

4y-26=-21x+42

21x+4y-68=0