Question

Please help ASAP. Differentiating polynomials

Answer 1

Answer:

Step-by-step 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

$y=25x +\frac{1}{x}$ then its derivative is

$y'=25-\frac{1}{x^2}$. This is equal to 0 where

$25-\frac{1}{x^2}=0$ and

$-\frac{1}{x^2}=-25$ or, in simpler terms:

$\frac{1}{x^2}=\frac{25}{1}$ so

$25x^2=1$ and

$x^2=\frac{1}{25}$ so

x = ±$\sqrt{\frac{1}{25} }$ so

x = $\frac{1}{5},- \frac{1}{5}$. When you plug those into the original equation, you get the coordinates

$(\frac{1}{5},10)$ and $(-\frac{1}{5},-10)$