Date | November 2019 | Marks available | 2 | Reference code | 19N.2.SL.TZ0.S_3 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | S_3 | Adapted from | N/A |
Question
Let f(x)=x−8, g(x)=x4−3 and h(x)=f(g(x)).
Find h(x).
Let C be a point on the graph of h. The tangent to the graph of h at C is parallel to the graph of f.
Find the x-coordinate of C.
Markscheme
attempt to form composite (in any order) (M1)
eg f(x4−3), (x−8)4−3
h(x)=x4−11 A1 N2
[2 marks]
recognizing that the gradient of the tangent is the derivative (M1)
eg h′
correct derivative (seen anywhere) (A1)
h′(x)=4x3
correct value for gradient of f (seen anywhere) (A1)
f′(x)=1, m=1
setting their derivative equal to 1 (M1)
4x3=1
0.629960
x=3√14 (exact), 0.630 A1 N3
[5 marks]