Question

Determine the slope of y=2x^2-4x+2.

Answer 1

Slope>?

Answer 2

Do you mean the derivative?

Answer 3

In this case, slope is gradient. this means you need to differentiate to make the quadratic equation into linear equation.
\[y=2x ^{2}-4x+2\]
\[dy/dy =4x-4\]
the slope is 4.

Hope this helps. Correct me if i'm wrong.

Answer 4

You're great yukitou. We haven't even remotely gone over derivatives. Could you tell me how you made the 2x^2 go away?

Answer 5

@sh3lsh , are you looking to find the solution using the difference quotient, or have you already learned the rule \(\large \frac{d}{dx} ax^n=nax^{n-1}\)

Answer 6

difference quotient.

Answer 7

Alright. Just for the record, the slope is not 4. But, I'll explain that later.

Answer 8

We shall take the difference quotient. Give me a moment to type it for this quadratic function.

Answer 9

\(\Huge \frac{f(x+\Delta x)-f(x)}{\Delta x}\)
First, I must make sure you know what this difference quotient even represents. Do you know?

Answer 10

Yes I do.

Answer 11

\(\huge \lim_{\Delta x->0}\frac{(2(x+\Delta x)^2-4(x+\Delta x)+2)-(2(x)^2-4(x)+2)}{\Delta x}.\)

Answer 12

Oh great. let me retype that -.-

Answer 13

hahaha! No no! I understand the point!

Answer 14

Anyways, I'm going to multiply this out lik a fool, because I completely forget how I used to evaluate the difference quotient with limits.

Answer 15

Haha, we did this in trig a bunch. I didn't know that derivative were tied in. You do NOT have to multiply it out!

Answer 16

difference quotient of 2x^2-4x+2
\(\huge \frac{2(x^2+2\Delta x+\Delta x^2)-4x-4\Delta x-2x^2+4x-2}{\Delta x}\)

Answer 17

difference quotient of 2x^2-4x+2
\(\huge \frac{2x^2+4\Delta x+2\Delta x^2-4x-4\Delta x-2x^2+4x-2}{\Delta x}\)

Answer 18

and the any term with h at the end is just thrown away right? I got 4x-4 :)

Answer 19

Gah, it's 4x-4

Answer 20

this is why we have the d/dx ax^n=ax^(n-1)

Answer 21

and d/dx (u+v)=d/dx u+d/dx v

Answer 22

I hate recreating the wheel lol

Answer 23

Haha, you helped a lot. Thanks again. So much.

Answer 24

Trust me, it's easier to just take the derivative in the future.

Answer 25

Sorry for the late reply.
How I made the 2x^2 go away?
Actually this is pretty straight forward after you do a lot of differentiation question.
\[y=2x ^{2}-4x+2\]
From this equation, you know you want to differentiate the equation. So you put the power 2 in front of the 2x.

Do you now why "2" of this y=2x^2 -4x=2 go?