Which statement is not true of the graph f(x)= (x+1)(x-3)^2?

Question

How do you solve this problem? Which is the right answer and why?

a) f has a relative maximum at (1/3, 256/27)

b) f has a point of inflection at (3,0)

c) f has an intercept at (3,0)

d) f has a relative minimum at (3,0)

e) none of these

Answer 1

f'(x) = (x - 3)(3x - 1), slope = 0 at x = 3, and x = 1/3.

f"(x) = 6x - 10, thus an inflection point at x = 5/3.

Since the only inflection point is x = 5/3, foil (b) is not true (false).

At (3, 0) the function has a minimum, determined by the (+) value of the second derivative (6[3] - 10) = 8