PPT-Tangent Line Problems

Find the equations of tangents at given points Find the points on the curve if tangent slope is known Find equations of tangents parallel to given lines through a given point Find equations of tangents . Notation dx dx y 00 f 00 Thus dx dx dy dx Example Find the second derivatives of the following functions a 2 x y 00 2 b y 00 c 5 4 5 y 00 The 64257rst derivative gives information about whether a funct ion increases or decreases In fact A d Pg 595. Circle. the set of all points equidistant from a given . point. Center. Congruent Circles. have . the same . radius. “Circle P” or . ○. P. Radius, r. the distance from the center to a point on . It can also be though. t. of as the locus of the end of a piece of string as the string is . wound/unwound. around the circumference of a plane figure. Involutes. Involutes are used to determine the length of belts used in pull. Tangent Lines. Average Rate of Change. The . average rate of change. of a quantity over a period of time is the slope on that interval of time.. Ex.:. . Find the average rate of change of . f(x) = x. 9.5 . Tangents to Circles. Objectives. Identify segments and lines related to circles.. Use properties of a tangent to a circle. .. Some definitions you need. Circle. – set of all points in a plane that are . Properties of Tangents. Geometry Honors. What and Why. What?. Find the relationship between a radius and a tangent, and between two tangents drawn from the same point.. Circumscribe a circle. Why?. To use tangents to circles in real-world situations, such as working in a machine shop.. Slope is the rate of change . or. . . Secant slope. the slope between two points. . tangent slope. the slope at one point of contact. and is based upon a limit.. Noun: derivative. Verb: differentiation or to. The slope of the secant line is given by. The tangent line’s slope at point a is given by. a. x. Example. Find the equation for the line tangent to the parabola . y = x. 2. at the point (1, 1). Another Form. Segments and Lines in relation to circles. Review of Terms and Ideas. Tangent. Line or segment that touches a circle at one point ( point of tangency). This line or segment is perpendicular to the radius at this point. Warm Up. Write the equation of each item.. 1.. . FG. . x. = –2. y. = 3. 2.. . EH. 3.. . 2(25 –. x. ). = x . 2. 4.. 3. x . 8. = . 4. x. x. = 16. x. = 8. Identify tangents, secants, and chords.. Alyssa Cobranchi. AP Calculus. Rectilinear Motion Introduction. Rectilinear Motion is the movement of a particle on a straight line.. It is an application of the derivative of a function.. Some examples can include a race car moving along a straight track, an object thrown from the top of a building and falling straight down, or a ball thrown straight up and then falling straight down.. NOW: . Replace: . Graph of . , with words:. Graph: (. , the . slope of the tangent line to the . function . . at that . point). .  . CALCULUS problem:. Graph: (. , the slope of the tangent line to the function . i.biza@uea.ac.uk This study focuses on a teaching experiment applied in a Year 12 class for the introduction of the derivative and the tangent line of function graph. This experiment was based on re Write the 3 steps to determine if a function is continuous . 1. ) F . is defined at c; that is, c is in the domain of f so that f(c) equals a #.. 2) . 3) . *So the same output is approached from both sides. .