Calculus

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y = f(x) = x^2 - 6 x

(a) Find the average rate of change of y with respect to x in the following intervals.
from x = 2 to x = 3
from x = 2 to x = 2.5
from x = 2 to x = 2.1

(b) Find the (instantaneous) rate of change of y at x = 2.

  • Calculus -

    to find the average slope between x = a and x = b

    average slope = [Y(b)-Y(a)] / [b-a]
    so for example from x = 2 to x = 3
    average slope = [ -9 - (-8) ] / [3-2]
    = -1

    for part b you want dy/dx at x = 2

    dy/dx = 2 x - 6
    = -2

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