2) Consider the function $f$ with second derivative $f''(x) = 3x - 1$. The graph of $f$ has a minimum point at $A(2, 4)$ and a maximum point at $B\left(-\frac{4}{3}, \frac{358}{27}\right)$.
a) Use the second derivative to justify that B is a maximum
b) Given that $f'(x) = \frac{3}{2}x^2 - x + p$, show that $p = -4$
c) Find $f(x)$.
3) A gradient function is given by $\frac{dy}{dx} = 10e^{2x} - 5$. When $x = 0$, $y = 8$. Find the value of y when $x = 1$.
4) Given that $\int_1^4 \frac{3}{3x + 2} dx = \ln k$, find the value of $k$.