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

(1)  y= square root of x

(2) y= 40x-16x^2

Jan 19th, 2015

Y= √x

f(x+h) =√(x+h)

f(x+h)-f(x) =√(x+h)- √x

[f(x+h)-f(x)]/h =(√(x+h)- √x)( √(x+h)+ √x)/[h(√(x+h)+ √x]

  = (x+h-x)/h *1/(√(x+h)+ √x]

  = (h)/h *1/(√(x+h)+ √x]

  = 1/(√(x+h)+ √x]

(2) y =40x-16x2

f(x+h)   = 40(x+h) -16(x+h)2

f(x+h)-f(x)   = 40 x+4oh -40x -16(x2+2xh+h2-x2)

  = 40h -16(2xh+h2)

[f(x+h)-f(x)]/h = 40 -32x-16h

Jan 19th, 2015

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