OCR PURE — Question 4 4 marks

Exam BoardOCR
ModulePURE
Marks4
PaperDownload PDF ↗
TopicDifferentiating Transcendental Functions
TypeFind gradient at a point - direct evaluation
DifficultyEasy -1.2 This is a straightforward two-part question testing basic exponential functions and differentiation. Part (a) requires simple logarithm manipulation (ln(10)/3), and part (b) requires routine differentiation of e^(3x) using the chain rule. Both are standard textbook exercises with no problem-solving or insight required, making this easier than average.
Spec1.06a Exponential function: a^x and e^x graphs and properties1.06d Natural logarithm: ln(x) function and properties1.07j Differentiate exponentials: e^(kx) and a^(kx)

A curve has equation \(y = e^{3x}\).
  1. Determine the value of \(x\) when \(y = 10\). [2]
  2. Determine the gradient of the tangent to the curve at the point where \(x = 2\). [2]

A curve has equation $y = e^{3x}$.

\begin{enumerate}[label=(\alph*)]
\item Determine the value of $x$ when $y = 10$. [2]

\item Determine the gradient of the tangent to the curve at the point where $x = 2$. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR PURE  Q4 [4]}}