1.33: Integrating an exponential and finding a second derivative

0606/12/M/J/17 — Question 11 · 8 marks

The curve y=f(x)y = f(x) passes through the point (12,72)\left(\dfrac{1}{2}, \dfrac{7}{2}\right) and is such that f′(x)=e2x−1f'(x) = \mathrm{e}^{2x - 1}.
(i)
Find the equation of the curve.
[4]
(ii)
Find the value of xx for which f′′(x)=4f''(x) = 4, giving your answer in the form a+bln⁡2a + b\ln\sqrt{2}, where aa and bb are constants.
[4]