OCR MEI Paper 3 2020 November — Question 11 2 marks

Exam BoardOCR MEI
ModulePaper 3 (Paper 3)
Year2020
SessionNovember
Marks2
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicDifferentiating Transcendental Functions
TypeShow stationary point exists or gradient has specific property
DifficultyEasy -2.5 This requires only recalling that d/dx(e^x) = e^x and observing that e^x > 0 for all x, therefore the derivative is always positive. This is a trivial one-step verification of a fundamental property, requiring no problem-solving or calculation beyond basic recall.
Spec1.07o Increasing/decreasing: functions using sign of dy/dx
11 Show that \(\mathrm { e } ^ { x }\) is an increasing function for all values of \(x\), as stated in line 39 .
Question 11:
AnswerMarks Guidance
AnswerMarks Guidance
\(\frac{dy}{dx} = e^x\)M1
Hence \(\frac{dy}{dx} > 0\) for all \(x\) so \(e^x\) is an increasing function for all \(x\)E1 Convincing completion (AG)
[2] 
## Question 11:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $\frac{dy}{dx} = e^x$ | M1 | |
| Hence $\frac{dy}{dx} > 0$ for all $x$ so $e^x$ is an increasing function for all $x$ | E1 | Convincing completion (AG) |
| **[2]** | | |

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11 Show that $\mathrm { e } ^ { x }$ is an increasing function for all values of $x$, as stated in line 39 .

\hfill \mbox{\textit{OCR MEI Paper 3 2020 Q11 [2]}}
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Q1 2 Q2 4 Q3 3 Q4 3 Q5 11 Q6 12 Q7 9 Q8 16 Q9 3 Q10 2 Q11 2 Q12 8