Posted by Anonymous on Friday, February 11, 2011 at 12:18pm.
f(x) = -1/2(x^2)
Step 1
f(x + h)= -1/2(x + h)^2
f(x + h)= -1/2(x^2 + 2xh + h^2)
f(x + h)= -1/2 x^2 - xh - 1/2 h^2
Step 2
f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 - (-1/2 x^2)
f(x + h)-f(x)= -1/2 x^2 - xh - 1/2 h^2 + 1/2 x^2
f(x + h) - f(x) = -xh - 1/2 h^2
f(x + h) - f(x) = h (-x - 1/2 h)
Step 3
(f(x + h) - f(x))/h = (h(-x - 1/2 h))/h
(f(x + h) - f(x))/h = -x - 1/2 h
Step 4
Evaluate lim h-->0
lim h-->0 = -x - 1/2 (0)
lim h-->0 = -x
Dx(-1/2 x^2) = -x
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