Find curve equation from derivative (exponential/logarithmic functions)

Given dy/dx or f'(x) involving exponential or logarithmic functions and a point on the curve, integrate to find y = f(x).

3 questions · Moderate -0.3

1.08c Integrate e^(kx), 1/x, sin(kx), cos(kx)
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CAIE P2 2013 June Q1
4 marks Moderate -0.8
1 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 4 } { 7 - 2 x }\). The point \(( 3,2 )\) lies on the curve. Find the equation of the curve.
CAIE P2 2005 November Q6
9 marks Moderate -0.8
6 A curve is such that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \mathrm { e } ^ { 2 x } - 2 \mathrm { e } ^ { - x }\). The point \(( 0,1 )\) lies on the curve.
  1. Find the equation of the curve.
  2. The curve has one stationary point. Find the \(x\)-coordinate of this point and determine whether it is a maximum or a minimum point.
AQA Paper 2 2018 June Q7
8 marks Standard +0.8
A function f has domain \(\mathbb{R}\) and range \(\{y \in \mathbb{R} : y \geq c\}\) The graph of \(y = f(x)\) is shown. \includegraphics{figure_2} The gradient of the curve at the point \((x, y)\) is given by \(\frac{dy}{dx} = (x - 1)e^x\) Find an expression for f(x). Fully justify your answer. [8 marks]