(Solved) For each function f(x) = 6x^2 - 4, estimate the instantaneous rate of change for the given values

marinejas

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3 years ago

For each function f(x) = 6x^2 - 4, estimate the instantaneous rate of change for the given values

of x.
a) x = -2 b) x = 0 c) x = 4 d) x = 8

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bio_man

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Educator

3 years ago

Are you doing calculus now?

Congrats!

⚠️⚠️Please watch this video, it is very important:⚠️⚠️

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marinejas Author

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3 years ago Edited: 3 years ago, marinejas

Hi and thanks! well yeah our last unit involves calculus, does that mean I have to post these type of questions in the calculus topic section? Just want to make sure but When I expanded the binomial from 6(x +△x)^2 in standard form, I got x^2 + 2△x +2△x + △x^2 or adding of the like terms, I get x^4 + 4△x + △x^2. Is that correct?

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bio_man

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Educator

3 years ago

Quote

Hi and thanks! well yeah our last unit involves calculus, does that mean I have to post these type of questions in the calculus topic section?

Yes, moving forward.

Quote

Just want to make sure but When I expanded the binomial from 6(x +△x)^2 in standard form, I got x^2 + 2△x +2△x + △x^2 or adding of the like terms, I get x^4 + 4△x + △x^2. Is that correct?

When you expand it, you get x2 + 2△x + △x2 (notice the middle terms △x combined to become 2△x). Then I multiplied it by 6.

PS: Watch the video.

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marinejas Author

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3 years ago

Oh yes sorry. Also, what do you mean by take limit? Just a bit confused at that step. And I will watch the video one I'm finished.

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bio_man

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Educator

3 years ago

Oh crap, you haven't learned limits yet? What about this:

I assumed that since you're learned rate of change, and instantaneous rate of change, you have learned it...

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marinejas Author

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3 years ago Edited: 3 years ago, marinejas

yes we have learned instantaneous rate of change! No, since we don't have much time left we're only focusing on 3 lessons, Average Rate of Change, instantaneous rate of change, and rates of change of other functions.

Post Merge: 3 years ago

we use the difference quotient formula

Post Merge: 3 years ago

sorry my mistake not that formula that you showed

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bio_man

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Educator

3 years ago

Could you show me an example of what your teacher has done? Maybe I can understand the situation better...

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marinejas Author

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3 years ago

Hi sorry, so here's an example, the question states, determine the instantaneous rate of change at x = 2 for the function f(x)= 5x^2-7

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bio_man

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marinejas Author

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#10

3 years ago

Oh okay, but for b) which is x = 0, the answer to that is 0, and this exactly what I did.
x=0
h= 0.001
1) f(0)= 6(0)^2-4 2) f(0+h)=6(1/1000)^2-4 3) f(0-h)=6(-1/1000)^2-4
= -4 = -3.999994 =-3.999994
(0, -4) (1/1000, -3.999994) (-1/1000, -3.999994)
4) IM= -3.999994-(-4)/-1/1000 - 0 5) IM= -3.99999-(-4)/1/1000 - 0 = 3/500
= -3/500

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bio_man

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#11

Educator

3 years ago

Here's what I get:

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marinejas Author

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#12

3 years ago

yeah the reason why I got it wrong was because you did 3.999, whereas I did 3.999994 (the full number from my calculator), but didn't know that would have affected my whole answer.

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bio_man

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#13

Educator

3 years ago

Are you taking another math course next semester?

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