WMA11 Jan 2019

6.​​ WMA11/01​​ Edexcel IAL P1 new January​​ 2019, Q6 (Differentiation)

(Solutions based entirely on graphical or numerical methods are not acceptable.)​​ 

Given​​ 

f(x) = 2x52  - 40x + 8        x > 0 

(a) solve the​​ equation f ʹ(x) = 0​​ 

(4)

(b) solve the equation f ʺ(x) = 5​​ 

(3)

SOLUTION

a-​​ Differentiating the given expression of​​ f(x).

fx=2x52-40x1+8

f'x=52x 2x32-40

f'x=5x32-40

Now, equating the equation to 0.​​ 

f ʹ(x) = 0

5x32-40=0

5x32=40

x32=8

x3223=823= 823

x=4

x32 =8

x3=8

x3=64

x= 643

x=4

b- ​​ First, integrating the f’(x) expression or in other words, finding the second​​ derivative.

f'x=5x32-40

f''x=152x12

Now, equating the expression to 5.​​ 

f''x=5

152x12=5

x12=1015

x12=23

x122=232

x=49