1.2 Rates of Change Using Equations
The difference quotient is:
The Instantaneous Rate of Change at x=a is estimated by calculating the slope of a secant over
a ≤ x ≤ a+h using a very small interval e.g. h=0.001.
Examples:
1. Determine the Average Rate of Change for 1 ≤ x ≤ 3 for the functions: f(x) = x+2
i)
By calculating the slope of the secant.
ii)
By using the Difference Quotient. Expand and simplify the DQ first.
a= _______
1.2
h= _______
1
2. Determine the Average Rate of Change for 1 ≤ x ≤ 3 for the functions: f(x) = 2x2 – 1
iii)
By calculating the slope of the secant
iv)
By using the Difference Quotient. Expand and simplify the DQ first.
a= _______
h= _______
3. Estimate the slope of the tangent line at x = 1 for the functions: f(x) = 2x2 – 1 by first simplifying
the difference quotient expression and then substituting h=0.1, h=0.01, and h=0.001 and
evaluating.
1.2
HW p.20 #1bd, 2, 4, 6, 7, 8, 12i, iii, 13b,d
2