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Date May 2012 Marks available 4 Reference code 12M.1.sl.TZ1.3
Level SL only Paper 1 Time zone TZ1
Command term Find and Show that Question number 3 Adapted from N/A

Question

Let \(f(x) = {{\rm{e}}^{6x}}\) .

Write down \(f'(x)\) .

[1]
a.

The tangent to the graph of f at the point \({\text{P}}(0{\text{, }}b)\) has gradient m .

(i)     Show that \(m = 6\) .

(ii)    Find b .

 

[4]
b(i) and (ii).

Hence, write down the equation of this tangent.

[1]
c.

Markscheme

\(f'(x) = 6{{\rm{e}}^{6x}}\)     A1     N1

[1 mark]

a.

(i) evidence of valid approach     (M1)

e.g. \(f'(0)\) ,  \(6{{\rm{e}}^{6 \times 0}}\)

correct manipulation     A1

e.g. \(6{{\rm{e}}^0}\) , \(6 \times 1\)

\(m = 6\)    AG     N0

(ii) evidence of finding \(f(0)\)     (M1)

e.g. \(y = {{\rm{e}}^{6(0)}}\)

\(b = 1\)     A1     N2

[4 marks]

b(i) and (ii).

\(y = 6x + 1\)     A1     N1

[1 mark]

c.

Examiners report

On the whole, candidates handled this question quite well with most candidates correctly applying the chain rule to an exponential function and successfully finding the equation of the tangent line.

a.

On the whole, candidates handled this question quite well with most candidates correctly applying the chain rule to an exponential function and successfully finding the equation of the tangent line. Some candidates lost a mark in (b)(i) for not showing sufficient working leading to the given answer.

b(i) and (ii).

On the whole, candidates handled this question quite well.

c.

Syllabus sections

Topic 6 - Calculus » 6.2 » Derivative of \({x^n}\left( {n \in \mathbb{Q}} \right)\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
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