WMA11 Jan 2019

12.​​ WMA11/01​​ Edexcel​​ IAL P1​​ January​​ 2019,​​ Q12​​ (Differentiation: Equations of Tangents &​​ Integration)

The curve with equation​​ y =f( x ), x > 0, passes through the point P(4,​​ −2).​​ 

Given that​​ 

dydx=3xx-10x-12

(a) find the equation of the tangent​​ to the curve at P, writing your answer in the form y = mx + c, where m and c are integers to be found.​​ 

(4)

(b) Find f( x ).​​ 

​​ (5)

SOLUTION

a-​​ To find the equation of the tangent to the curve, we need to find the gradient of the tangent to use the point-slope formula. So, first finding the gradient of the tangent of the curve at point P.​​ 

dydx=3x x-10 x

dydxx=4=344-104

dydxx=4==24-5=19

Hence, the gradient of tangent at point P is 19 whereas the point is (4,-2). Now, using point-slope formula.​​ 

y-y!=mx-x1

y--2=19x-4

y+2- 19x-76

y=19x-78

b-​​ 

To find the function f(x), we need to integrate​​ the expression of f’(x) as integration is anti-derivative.

fx=∫3x32-10x-12dx

fx=3x5252 -10x1212+c

fx=65x52-20x12+c

To find the value of c, substitute the point P (4,-2) as it is a point on a curve and would satisfy the equation of curve.​​ 

-2=6545-204+c

-2=6532-40+c

c=38-1925

c=-25

Hence, the equation is​​ 

fx=65x3-20x12-25