Question 1

Paper 1, no calculatorMedium6 marks

In Figure 1, the solid curve is y=g(x)y=g(x) The dashed line is its tangent at PP where x=0x=0

-1120123456789101112xg(x)P
(a)

Using Figure 1, write down the values of g(0)g(0) and g′(0)g'(0)

[2]
(b)

The function FF is defined by

F(x)=eg(x)x+2.F(x)=\frac{e^{g(x)}}{x+2}.

Determine F′(0)F'(0) giving your answer exactly.

[4]

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