Question

Please help ASAP. Differentiating polynomials

Answer 1

Explanation:

If the function is

`y=x^2-4x`, then its derivative is

y' = 2x - 4. This is equal to 0 where

2x - 4 = 0 and

2x = 4 so

x = 2. When x = 2 in the original equation:

`y =2^2-4(2)` so

y = -4. So the coordinate is (2, -4). On to the next one:

If the function is

`y=25x +(1)/(x)` then its derivative is

`y'=25-(1)/(x^2)`. This is equal to 0 where

`25-(1)/(x^2)=0` and

`-(1)/(x^2)=-25` or, in simpler terms:

`(1)/(x^2)=(25)/(1)` so

`25x^2=1` and

`x^2=(1)/(25)` so

x = ±
`\sqrt{(1)/(25) }` so

x =
`(1)/(5),- (1)/(5)`. When you plug those into the original equation, you get the coordinates

`((1)/(5),10)` and
`(-(1)/(5),-10)`