Delta Question: What is the slope of the function y = x2 at x = 3 ?

ManolitoAguirre

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What is the slope of the function y = x2 at x = 3 ?

At x = 3, y = 32 = 9

At x = (3 + Δx), y = (3 + Δx)2 = 9 + 6Δx + (Δx)2

The difference between the y values from x = 3 to x = (3 + Δx)
= 9 + 6Δx + (Δx)2* − 9
= 6Δx + (Δx)2*

Now we can calculate the slope:


As Δx shrinks towards zero we are left with:
Slope = 6


I did this question on Mathopolis. Question is: in the middle of the equation, did the 6 come from adding 3 and 3?

Thank you for your help!

:)

Sent from my SM-T560NU using Tapatalk
 
What is the slope of the function y = x^2 at x = 3 ?

At x = 3, y = 3^2 = 9

At x = (3 + Δx), y = (3 + Δx)^2 = 9 + 6Δx + (Δx)^2

The difference between the y values from x = 3 to x = (3 + Δx)
= 9 + 6Δx + (Δx)^2* − 9
= 6Δx + (Δx)^2*

Now we can calculate the slope:


As Δx shrinks towards zero we are left with:
Slope = 6


I did this question on Mathopolis. Question is: in the middle of the equation, did the 6 come from adding 3 and 3?

Note that I have inserted ^ in your expressions above to indicate exponents.

Yes, the 6 comes from doing this:

(3 + Δx)^2 = (3 + Δx)(3 + Δx) = 3*3 + 3Δx + 3Δx + (Δx)^2 = 9 + 6Δx + (Δx)^2

We commonly save work by using the formula

(a + b)^2 = a^2 + 2ab + b^2

which is derived the same way.
 
What is the slope of the function y = x2 at x = 3 ?

At x = 3, y = 32 = 9

At x = (3 + Δx), y = (3 + Δx)2 = 9 + 6Δx + (Δx)2

The difference between the y values from x = 3 to x = (3 + Δx)
= 9 + 6Δx + (Δx)2* − 9
= 6Δx + (Δx)2*

Now we can calculate the slope:


As Δx shrinks towards zero we are left with:
Slope = 6


I did this question on Mathopolis. Question is: in the middle of the equation, did the 6 come from adding 3 and 3?

Thank you for your help!

:)

Sent from my SM-T560NU using Tapatalk
No - it came from:

(a + b)2 = a2 + b2 + 2*a*b
 
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