Mathematics

Problem

Let

g(x)=ax^2-3x+1

and

h(x)=2x^3+x^2-4

. Define the polynomial

P(x)=g(h(x))

. a. Part 1: (i) Expand

P(x)

and write it in standard descending-power form. b. Part 2: (ii) Find the derivative

P'(x)

. c. Part 3: (iii) If

P'(1)=0

, determine the value of the parameter

a