advertisement

SOLVING PROBLEMS USING RATES of CHANGE (Max & Min) Introduction It is often useful to use rates of change to determine the maximum or minimum values of a function. y y local max absolute min x x absolute max local min The slope of the tangent line at the max/min point is 0!! If the slope of the tangent is negative to the left of the point and positive to the right of the point, then a minimum exists at that point. –ve +ve m=0 at min If the slope of the tangent is positive to the left of the point and negative to the right of the point, then a maximum exists at that point. m=0 at max +ve –ve Example Use an algebraic strategy to verify that the point (–2, –25) is either a maximum or minimum of the function, f(x) = x2 + 4x – 21. Example Determine the equation of the tangent line to the curve, f(x) = x2 – 3x + 1, at the point where x = –2. Example A golf shot is modelled by the function, H(t) = –5t2 + 40t, where H(t) is the height of the golf ball in metres and t is the time that it is in the air in seconds. Estimate the time at which the golf ball will be at a maximum height above the ground. Homework: p.112–113 #5ac, 6ab, 7, 10, 11