let f(x) be the function 4x^2 -10x+6. then the quotient [f(8+h)-f(h)]/h can be simplified to ah+b for: a=? b=?

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beckden | High School Teacher | (Level 1) Educator

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`f(x)=4x^2-10x+6 `

`f(8+h) = 4(8+h)^2 - 10(8+h) + 6 = 4(64 + 16h + h^2) - 80 - 10h + 6 = 256 + 64h + 4h^2 - 74 - 10h`

`f(8+h) = 4h^2 + 54h + 182`

`f(8) = 4(8^2) - 10(8) + 6 = 256 - 80 + 6 = 182`

`f(8+h) - f(h) = 4h^2 + 54h + 182 - (182) = 4h^2 + 54h`

 

`(f(8+h) - f(h))/h = (4h^2 + 54h)/h = 4h + 54 `

So a=4, b=54

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