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# Let f(x) be the function `2x^2-10x+4` , the quotient `(f(10+h)-f(10))/h` can be...

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Let f(x) be the function `2x^2-10x+4` , the quotient `(f(10+h)-f(10))/h` can be simplified ah+b for a=? and b=?

Posted by adb2188 on January 23, 2013 at 12:42 AM via iOS and tagged with calculus, math

High School Teacher

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

To solve for `(f(10+h)-f(10))/h` , determine f(10+h) first.

`f(10+h) = 2(10+h)^2-10(10+h)+4`

`f(10+h)= 2(10+h)(10+h)-100-10h+4`

`f(10+h)=2(100+20h+h^2)-100-10h+4`

`f(10+h)=200+40h+2h^2-100-10h+4`

`f(10+h)=2h^2+30h+104`

Evaluate f(10) too.

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

`f(10)=2*100-100+4`

`f(10)=104`

So we have,

`(f(10+h)-f(10))/h = (2h^2+30h+104 - 104)/h`

`(f(10+h)-f(10))/h = (2h^2 + 30h)/h`

To simplify, factor the numerator and cancel common factor.

`(f(10+h)-f(10))/h = (2h(h+15))/h`

`(f(10+h)-f(10))/h = 2(h+15)`

`(f(10+h)-f(10))/h = 2h+ 30`

Hence, a=2 and b=30 .

Posted by mjripalda on January 23, 2013 at 2:09 AM (Answer #1)

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