Calculus techniques to establish the first and second

Question

Use calculus techniques to establish the first and second derivatives of the following functions and to graph the functions below by indicating

1) points where f(x) = 0,

2) the y-intercept,

3) all relative maxima,

4) all relative minima, and 4) points of inflection, if any.

Show all of your work.

a) f(x) = x²/x+1

b) f(x) = x³ + 3x² + 3x

c) f(x) = (5x² + 6x - 2)(x - 5)