The function y = 3x - 4x^2 + 2. The value of derivative of the function `dy/dx` at any point gives the slope of the tangent at that point. At extreme points the slope of the tangent is 0 and it has opposite signs on either sides of this point.
For y = 3x - 4x^2 + 2, `dy/dx = 3 - 8x`
`dy/dx = 3 - 8x = 0`
=> `x = 3/8`
The second derivative of the function is -8. As this is negative, the extreme point is a point of maximum.
At x = `3/8` , y = `41/16`
The function has a point of maximum at (`3/8, 41/16` )