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Date November 2021 Marks available 1 Reference code 21N.1.SL.TZ0.5
Level Standard Level Paper Paper 1 (without calculator) Time zone Time zone 0
Command term Find Question number 5 Adapted from N/A

Question

The function f is defined for all x. The line with equation y=6x-1 is the tangent to the graph of f at x=4.

The function g is defined for all x where gx=x2-3x and hx=fgx.

Write down the value of f(4).

[1]
a.

Find f(4).

[1]
b.

Find h(4).

[2]
c.

Hence find the equation of the tangent to the graph of h at x=4.

[3]
d.

Markscheme

f'(4)=6               A1

 

[1 mark]

a.

f(4)=6×4-1=23               A1

 

[1 mark]

b.

h4=fg4                 (M1)

h4=f42-3×4=f4

h4=23                 A1

 

[2 marks]

c.

attempt to use chain rule to find h'                 (M1)

f'gx×g'x   OR   x2-3x'×f'x2-3x

h'4=2×4-3f'42-3×4                 A1

         =30 

y-23=30x-4   OR   y=30x-97                 A1

 

[3 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Topic 2—Functions » SL 2.1—Equations of straight lines, parallel and perpendicular
Topic 5 —Calculus » SL 5.4—Tangents and normal
Topic 2—Functions » SL 2.5—Composite functions, identity, finding inverse
Topic 5 —Calculus » SL 5.6—Differentiating polynomials n E Q. Chain, product and quotient rules
Topic 2—Functions
Topic 5 —Calculus

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