'Line tangent' presentation slideshows

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The Derivative and the Tangent Line Problem

The Derivative and the Tangent Line Problem. Section 2.1. After this lesson, you should be able to:. find the slope of the tangent line to a curve at a point use the limit definition of a derivative to find the derivative of a function

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CHAPTER 5 SECTION 5.4 EXPONENTIAL FUNCTIONS: DIFFERENTIATION AND INTEGRATION

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The Derivative

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AB Calculus

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Section 2.3 Product & Quotient Rules and Higher-Order Derivatives

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Continuation of Lecture 2

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Section 10.1

Section 10.1 . Circles. 10.1 Notes. What is a CIRCLE? A CIRCLE is the set of all points in a plane equidistant from a given point. . 10.1 Notes. There are points ON , IN , and OUTSIDE the circle. The points in the circle make up the INTERIOR of the circle. . 10.1 Notes.

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The derivative as the slope of the tangent line

The derivative as the slope of the tangent line. (at a point). What is a derivative ?. A function the rate of change of a function the slope of the line tangent to the curve. The tangent line. single point of intersection. slope of a secant line. f(a) - f(x). a - x. f(x). f(a). x.

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pg 651

pg 651 . A chord is a line segment with each endpoint on the circle. A diameter is a chord that passes through the center of the circle. A secant of a circle is a line that intersects a circle at exactly two points. 1. Draw a chord. 2. Draw a diameter. 3. Draw a secant .

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Consider the region bounded by the curve r = f ( ? ) and the two rays

Integration in polar coordinates involves finding not the area underneath a curve but, rather, the area of a sector bounded by a curve . . Consider the region bounded by the curve r = f ( ? ) and the two rays.

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5.1 DERIVATIVES OF EXPONENTIAL FUNCTIONS

5.1 DERIVATIVES OF EXPONENTIAL FUNCTIONS. By: Rafal, Paola , Mujahid. RECALL:. y=e x (exponential function) LOGARITHM FUNCTION IS THE INVERSE EX1: y=log 4 x y=4 x Therefore y=e x y=log e x. IN THIS SECTION:.

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EXAMPLE 1

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Finding the Derivative

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Angles, Circles, and parts of Circles

Angles, Circles, and parts of Circles. secant: a line, ray, or segment that contains a chord chord: segment has endpoints on circle t angent: a line, ray, or segment that touches the circle in one point. Tangent: a line, ray, or segment that only intersects the circle at one point.

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Polar Derivatives

Polar Derivatives. Section 10-4 continued. Slope and Tangent Lines. To find the slope of a tangent line to a polar graph, consider a differentiable function given by r = f ( ? ). To find the slope in polar form, use the parametric equations x = r cos ? = f ( ? ) cos ? and

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Derivatives of Parametric Equations

Derivatives of Parametric Equations. Lesson 10.2. Studying Graphs. Recall that a function , y = f(x) is intersected no more than once by a vertical line Other graphs exist that are not functions We seek to study characteristics of such graphs

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Differentiation in Polar Coordinates

Differentiation in Polar Coordinates. Lesson 10.7. Review. Relationship of polar and rectangular systems x = r cos ? y = r sin ? Given r = f( ? ), simple to find dr/d ? However, we seek dy/dx . Finding dy/dx. We know r = f( ? ) and y = r sin ? and x = r cos ? Then And .

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Equation of Tangent line

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