calculus please help
posted by Anonymous .
Use the four step process to find the slope of the tangent line to the graph at any point:
f(x) = 1/2(x^2)

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