determine slope of y=2x^2 - 4x + 2

**apm** · August 23rd 2008, 11:38 AM

i have to determine the slope of y=2x^2 - 4x +2

isn't that a parabola? how can it have a slope or does it have two different ones? but how can a curve have a slope?

there is also another problem similar to this
y=x^2 from (-1,1) to (x,y) and it wants me to determine change in y/change in x in terms of x

Thanks!

**skeeter** · August 23rd 2008, 11:46 AM

start here for an introductory lesson ...

The Slope of a Curve ... an Introduction to Derivative Calculus .........

**apm** · August 23rd 2008, 11:48 AM

thank you

**Chris L T521** · August 23rd 2008, 11:55 AM

Originally Posted by apm

i have to determine the slope of y=2x^2 - 4x +2

isn't that a parabola? how can it have a slope or does it have two different ones? but how can a curve have a slope?

If we were to look for a tangent line, we end up differentiating the function. This gives us the slope of the function. However, the function has an infinite number of slopes, unless a particular x value is specified.

In our case, $y=2x^2-4x+2$ .

When we differentiate it, we get $y'=4x-4$

This is our slope. Since there is no x value specified, there are an infinite number of slopes values that depend on the value of x, where $x\in\mathbb{R}$ .

there is also another problem similar to this
y=x^2 from (-1,1) to (x,y) and it wants me to determine change in y/change in x in terms of x

Thanks!

I would assume that they are requesting the average slope...

The line is defined over the interval $(-1,x_0)$

Thus, $\frac{\Delta y}{\Delta x}=\frac{f(b)-f(a)}{b-a}\implies \frac{\Delta y}{\Delta x}=\frac{x_0^2-1}{x_0+1}\implies\color{red}\boxed{\frac{\Delta y}{\Delta x}=x_0-1}$

I hope this makes sense.

--Chris

**KSiimson** · January 31st 2009, 10:04 PM

Sorry for posting in a kind-of-old thread, but I have the same problem and I can't figure it out. The posted problem does not give a particular point to find the slope of.

Are there any examples of solving such problems, step by step and preferably with explanations?

p.s! I hope its not too difficult to understand what I just typed, my first language has loose word order and I just spent half a day translating to that. :P

e: Thanks to mr. fantastic for rewording my post. I got

. What will happen to 2h?

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