| Date | November 2021 | Marks available | 3 | Reference code | 21N.1.SL.TZ0.5 |
| Level | Standard Level | Paper | Paper 1 (without calculator) | Time zone | Time zone 0 |
| Command term | Hence and Find | Question number | 5 | Adapted from | N/A |
Question
The function f is defined for all x∈ℝ. 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∈ℝ where g(x)=x2-3x and h(x)=f(g(x)).
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.
h(4)=f(g(4)) (M1)
h(4)=f(42-3×4)=f(4)
h(4)=23 A1
[2 marks]
c.
attempt to use chain rule to find h' (M1)
f'(g(x))×g'(x) OR (x2-3x)'×f'(x2-3x)
h'(4)=(2×4-3)f'(42-3×4) A1
=30
y-23=30(x-4) OR y=30x-97 A1
[3 marks]
d.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
