| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Product & Quotient Rules |
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13. The function \(g\) is defined by
$$\mathrm { g } ( x ) = \frac { 2 e ^ { x } - 5 } { e ^ { x } - 4 } \quad x \neq k , x > 0$$
where \(k\) is a constant.
a. Deduce the value of \(k\).
b. Prove that
$$\mathrm { g } ^ { \prime } ( x ) < 0$$
For all values of \(x\) in the domain of g .
c. Find the range of values of \(a\) for which
$$\mathrm { g } ( a ) > 0$$