Assignment:
Q1. (a) Let f(x)=ax^2+bx+c, a does not equal zero, be a quadratic polynomial. How many points of inflection does the graph of f have?
(b)Let f(x)=ax^3+bx^2+cx+d, a does not equal zero, be a cubic polynomial. How many points of inflection does the graph of f have?
(c) Suppose the function y=f(x) satisfies the equation dy/dx=ky(L-y), where k and L are positive constants. Show that the graph of f has a point of inflection at the point where y=L/2.
Q2. Let f(x)=c/x+x^2. Determine all values of the constant c such that f has a relative minimum, but no relative maximum.
Provide complete and step by step solution for the question and show calculations and use formulas.