Ontario Virtual School (Online E-Learning High School)

MCV4U

Courses > Sample Lessons

Ministry Expectations
Specific Expectations:
A1.5 make connections, for a function that is smooth over the interval a [lesser than or equal to symbol] x [lesser than or equal to symbol] a + h, between the average rate of change of the function over this interval and the value of the expression f(a + h) – f(a)/h , and between the instantaneous rate of change of the function at x = a and the value of the limit lim[h arrow 0] f(a + h) – f(a)/h
A1.6 compare, through investigation, the calculation of instantaneous rates of change at a point (a, f(a)) for polynomial functions [e.g., f(x) = x(2), f(x) = x(3)], with and without f(a + h) – f(a)/h simplifying the expression before substituting values of that approach zero [e.g., for f(x) = x(2) at x = 3, by determining f(3 + 1) – f(3)/1 = 7, f(3 + 0.1) – f(3) = 6.1, f(3 + 0.01) – f(3)/0.01 = 6.01, and f(3 + 0.001) – f(3)/001 = 6.001, and by first simplifying f(3 + h) – f(3)/h as (3 + h)2 – 3(2)/h = 6 + h and then substituting the same values of h to give the same results]