Let $$a$$ be a real number such that the function $$f(x) = ax^2 + 6x - 15$$, $$x \in R$$ is increasing in $$\left(-\infty, \frac{3}{4}\right)$$ and decreasing in $$\left(\frac{3}{4}, \infty\right)$$. Then the function $$g(x) = ax^2 - 6x + 15$$, $$x \in R$$ has a

A

local maximum at $$x = -\frac{3}{4}$$

B

local minimum at $$x = -\frac{3}{4}$$

C

local maximum at $$x = \frac{3}{4}$$

D

local minimum at $$x = \frac{3}{4}$$