MCV 4U - Chapter 1 EXIT SLIP#1 NAME: 1) (a) Calculate the slope of the tangent to / (x) = - at x = 4. (b) Determine the equation of the tangent at x = 4 2) A toy rocket is launched in the air so that its height, s, at time : is measured by s () =- 5r- + 30r+ 2. What is the instantaneous velocity at 4 seconds?ate vivpe Ul a iangent ing Goal: To determine the slope of a tangent line at a point on the graph of a given function. ALL: Slope of a Line SLOPE OF A TANGENT: The slope of the tangent to a curve at a point P is the my_ yz y1 limiting slope of the secant PQ as the point Q slides QQo 4x X2 -X along the curve toward P. In other words, the slope tangent at P of the tangent is said to be the limit of the slope of inear relations, the slope or rate of change remains the secant as Q approaches P along the curve. secant tant. 4/ P Ly = f(x) t about NON-LINEAR RELATIONS? mtangent = lim (slope of secant PQ) Q -P h +0 e of a Secant Line of a Curve Slope of a Tangent Line of a Curve at an arbitrary point The line PQ is a secant line. y = f (xc) The tangent line is a line that touches a curve at a single point in a small The slope of the secant is the average rate of change region. of the function between 2 points. The slope of the tangent represents the instantaneous rate of change of 3C 2 92 Q(a + h, fla + h)) the curve at that point. * derivative 7 secant specific point tangent The slope of the tangent to the graph y=f (x ) at point P(a, f (a)) is at P by = f ( x ) m lim Ay lim flath ) - fla) if the " tangent Ax -0 Ax : hoo limit 12 : P(a, fla)) h exists -ath Alternate form for specific P ( a, * (a ) ) Ay flash ) - f ( a ) m t lim . f (x ) - fla) m secant ac - a a + h - a OC - a m f ( a . h ) - i ( @ ) Difference my = " lim f ( oc + h ) - f ( xc) for any h Quotient h point along + curve Scanned with CamScanner