Give the extreme points of y = 3x - 4x^2 + 2. Are they maximum of minimum?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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` )

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