calculus

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Find the following limit where f(x) = 4x2 − 3x.

limit
delta x --> f(x + delta x)- f(x)/delta x

can someone please help me

  • calculus -

    I assume you mean the limit as delta x -> 0.
    I'll use delta x = h for simplicity

    (f(x + h) - f(x))/h
    = (4(x+h)^2 - 3(x+h) - (4x^2 - 3x))/h
    = (4x^2 + 8xh + 4h^2 - 3x - 3h - 4x^2 + 3x)/h
    = (8xh + 4h^2 - 3h)/h
    = 8x - 3 + 4h

    Limit as h->0 = 8x-3

    Looks like the derivative, eh?

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