I need help, but it's not urgent haha :)

Question

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Given the function f(x) = 4x^2 - 10x + 9, What is the average rate of change for f ove rthe interval 2.6 le x le 5.2?

(le means less than or equal too btw :))

Thank you so, so much if you can take any time to help me, if not that's ok too though

hectictar · Answer 1 · 2019-11-15T04:21:35

The average rate of change of f over the interval 2.6 ≤ x ≤ 5.2 is the slope of the blue dotted line on the above graph.

The blue dotted line passes through the purple point, (2.6, f(2.6)) , and the green point, (5.2, f(5.2))

Do you know how to find the slope of the blue dotted line? (Remember "rise over run" )

ANotSmartPerson · Answer 2 · 2019-11-15T04:44:30

Uhhh I think I did something wrong :PP I got (15-5)\(3-2) = 10 as the slope but I don't think that's right.. :((

CPhill · Answer 3 · 2019-11-15T05:22:12

f(2.6) = 4(2.6)^2 - 10(2.6) + 9 = 10.04

f(5.2) = 4(5.2)^2 - 10(5.2) + 9 =65.16

So we have the points ( 2.6, 10.04) and ( 5.2, 65.16)

The slope is

[ 65.16 - 10.04 ] / [ 5.2 - 2.6 ] = 21.2 = avg rate of change

ANotSmartPerson · Answer 4 · 2019-11-18T12:47:06

Thanks Phil! I get it now lol :))