WMA11 Jan 2021

7. WMA11/01​​ Edexcel​​ IAL P1 January 2021 IAL Q7​​ (Quadratic: Solving Quadratic Equations &​​ Differentiation)

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

Solutions relying on calculator​​ technology are not acceptable.

fx = 2x-3x-5          x>0

• Solve the equation​​ 

f(x) = 9 

(4)

• Solve the equation​​ 

f″ x= 6 

(5)

SOLUTION

a-​​ 

2x-3x-5=9

2x-3x-14=0

Let​​ t=x, so​​ t2=x, where t > 0

2t2-3t-14=0

2t-7t+2=0

2t=7

t=72     t=-2

Substituting back​​ t=x, and​​ t2=x

x=72x=-2 (Rejected)

√x=-2 rejected because t >​​ 0.

x=494

b-

fx=2x-3x12-5

f'x=2-32x-12

f''x=34x-32

Now, it is given that​​ f''x=6, so equating the second derivative expression to 6.

34x-32=6

34x32=6

34 x 6=x32

18=x32

x32=18

x3 =18

Squaring both sides

x3 2=182

x3=182

x=1823

x=122

x=14