Question

Is `f(x)=(-2x^2-5x-2)/(2x-4)` increasing or decreasing at `x=0`?

Answer 1

Take the first derivative and see if the slope is positive or negative

Explanation:

Use the quotient rule to take the first derivative, so `u/v` = `(vdu-udv)/v^2`. u = `-2x^2-5x-2` du = `-4x-5` v = 2x-4 dv = 2

Then, `((2x-4)*(-4x-5)-(-2x^2-5x-2)*2)/((2x-4)^2)`

Then `(-8x^2+16x-10x+20+4x^2+10x+4)/(4x^2-16x+16)`

At x = 0, this becomes 24/16 which is positive, so increasing.