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Qnexyrbcneq4

Mathematics

Description

Simplify the difference quotient f(x+h) - f(x) all over h.  

(1)  y = 4x - x^2

(2) f(x)= 2x + 1 over x + 3

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Explanation & Answer

 y = 4x - x2

f(x+h) = 4(x+h)-(x+h)2

f(x+h)-f(x) = 4(x+h)-(x2+2hx+h2)- 4x +x2 = 4h -2hx-h2

[f(x+h)-f(x)]/h = 4-2x-h

(2) f(x)= 2x + 1 over x + 3

f(x) = (2x+1)/(x+3)

f(x+h) = (2x+2h+1)/(x+h+3)

f(x+h)-f(x) = (2x+2h+1)/(x+h+3) –(2x+1)/(x+3)

  =[ (2x+2h+1)(x+3) –(2x+1)(x+h+3)]/[(x+h+3)(x+3)]

  =[ (2x+1)(x+3) +2h(x+3) –(2x+1)(x+3) -h(2x+1)]/[(x+h+3)(x+3)]

  = h(2x+6-2x-1)/ [(x+h+3)(x+3)]

  = 5h/[(x+h+3)(x+3)]

[f(x+h)-f(x)]/h = 5/[(x+h+3)(x+3)]



Anonymous
Just what I needed…Fantastic!

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