Determine the average rate of change of the function over theintervalb) Copy the graph, and draw a tangent line at the point whereDetermine the slope of the tangent line to estimate theinstantaneous rate of change at this point.2. Estimate the instantaneous rate of change of the function inquestion 1 at by determining the slope of a secant line fromthe point where to the point where Compare youranswer with your answer for question 1, part b).3. Use graphing technology to estimate the instantaneous rate of changeof the function in question 1 atPRACTISING4. Estimate the instantaneous rate of change of at thepoint (2, 21).f (x) 5 xx 2 4x 5 2.x 5 2.01.x 5 2x 5 2x 5 2.2 # x # 7.In SummaryKey Ideas• The methods that were previously used to calculate the average rate of changeand estimate the instantaneous rate of change can be used for rationalfunctions.• You cannot determine the average and instantaneous rates of change of arational function at a point where the graph is discontinuous (that is, wherethere is a hole or a vertical asymptote).Need to Know• The average rate of change of a rational function, on the intervalfrom is Graphically, this is equivalent to the slopeof the secant line that passes through the points and on thegraph of• The instantaneous rate of change of a rational function, at canbe approximated using the difference quotient and a very smallvalue of h. Graphically, this is equivalent to estimating the slope of the tangentline that passes through the point on the graph of• The instantaneous rate of change at a vertical asymptote is undefined. Theinstantaneous rates of change at points that are approaching a verticalasymptote become very large positive or very large negative values. Theinstantaneous rate of change near a horizontal asymptote approaches zero.y 5 f(x).(a, f(a))f(a 1 h) 2 f(a)hx 5 ay 5 f(x),y 5 f(x).(x2, y2)(x1, y1)f(x2) 2 f(x1)x2 2 x1 .x1 # x # x2y 5 f(x),01010–10–10yxy = x + 2——–-x – 1NEL 303Chapter 55.6