# Differentiation/graphs

I have two problems (well, one problem with three parts and another one):

1. (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.

7. 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.

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