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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)=x8,  g(x)=x43  and  h(x)=f(g(x)).

Find h(x).

[2]
a.

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.

[5]
b.

Markscheme

attempt to form composite (in any order)        (M1)

eg       f(x43),  (x8)43

h(x)=x411       A1  N2

[2 marks]

a.

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=314 (exact),  0.630       A1  N3

[5 marks]

b.

Examiners report

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

Syllabus sections

Topic 5 —Calculus » SL 5.3—Differentiating polynomials, n E Z
Show 91 related questions
Topic 5 —Calculus » SL 5.4—Tangents and normal
Topic 2—Functions » SL 2.5—Composite functions, identity, finding inverse
Topic 2—Functions
Topic 5 —Calculus

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