for part (b), obviously you use the Newton-Raphson method. you can find out how to use it here
(a) Plot the graph of f (x) = 3x + 2x^2-x^3-5 over the interval [0, 3] using 0.2 as a step
size. From the graph estimate the smaller of the two roots of f (x) = 0 . (This should be
correct to 1 decimal place.)
(b) Use the Newton-Raphson method to find an approximation to the smaller positive root
of f (x) = 0 correct to 7 decimal places.