calculus

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using f'(x) as the limit of h approaches 0 [f(x+h)-f(x)]/h
find: f'(x), given f(x)=|x|

  • calculus -

    the graph of f(x) = |x|
    is a V with the vertex at the origin.
    (made up of y = x in quadrant I and y = -x in quadrant II)
    your two graphs are y = x and y = -x
    I will do the second part as x ---> 0 for y = -x
    = lim (-(x+h) - (-x))/h as x ---> 0
    = lim (-x - h + x)/h as x--> 0
    = lim -h/h
    = -1

    do the same with f(x) = y = x to show
    a result of +1

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