Find the value of x for which the expression $$2 - 3x- 4x^{2}$$ has the greatest value.

NOTE :- To find the min/max value of an expression, we need to differentiate it, and put the first derivative equal to '0' to find value of $$x$$

Then, we need to differentiate it again and put value of $$x$$, if second derivative is less than zero, then $$x$$ is maxima otherwise $$x$$ is minima.

Expression : $$y$$ = $$2 - 3x- 4x^{2}$$

=> $$\frac{dy}{dx} = -3 - 8x$$

Now, putting it equal to 0, we get :

=> $$y' = -3 -8x = 0$$

=> $$x = \frac{-3}{8}$$

Differentiating it again :

=> $$\frac{d^2y}{dx^2} = -8$$

Since, it is less than '0' ,=> $$x = \frac{-3}{8}$$ is maximum value.