3-5 Higher Derivatives Tues Oct 20 Do Now Find the velocity at t = 2 for each position function 1) 2)

Slides:

Advertisements

Similar presentations

Summer Assignment + R Quiz Review Fri Sept 12 Do Now Simplify the complex rational expression.

Advertisements

2.2 Complex Numbers Fri Feb 20 Do Now 1) 2x^2 -8 = 0 2) (sinx)^2 – 2sinx + 1 = 0.

6.1 Area Between 2 Curves Wed March 18 Do Now Find the area under each curve in the interval [0,1] 1) 2)

2 nd Derivatives, and the Chain Rule (2/2/06) The second derivative f '' of a function f measures the rate of change of the rate of change of f. On a graph,

4.9 Antiderivatives Wed Feb 4 Do Now Find the derivative of each function 1) 2)

8.2 Systems of Equations in Three Variables Day 1 Fri May 1 Do Now Solve the system.

4.3 Logarithmic Functions and Graphs Do Now Find the inverse of f(x) = 4x^2 - 1.

4.6 Curve Sketching Thurs Dec 11 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of.

3.9 Exponential and Logarithmic Derivatives Wed Nov 12 Do Now Find the derivatives of: 1) 2)

Every slope is a derivative. Velocity = slope of the tangent line to a position vs. time graph Acceleration = slope of the velocity vs. time graph How.

4.9 Antiderivatives Wed Jan 7 Do Now If f ’(x) = x^2, find f(x)

Do Now Find the derivative of each 1) (use product rule) 2)

2.3 The Product and Quotient Rules and Higher Order Derivatives

Quick Quiz Consider the graph at the right. The object whose motion is represented by this graph is ... (include all that are true): moving in the positive.

2.6 Trigonometric Limits Fri Sept 25 Do Now Evaluate the limits.

AP Calculus BC Monday, 14 September 2015 OBJECTIVE TSW (1) define the slope of a curve at a point, and (2) define the derivative. Tests are graded. TODAY’S.

3.1 The Derivative Tues Sept 22 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4.

Product & quotient rules & higher-order derivatives (2.3) October 17th, 2012.

3.9 Exponential and Logarithmic Derivatives Thurs Oct 8

2-1 The Derivative and the Tangent Line Problem 2-2 Basic Differentiation Rules and Rates of Change 2-3 Product/Quotient Rule and Higher-Order Derivatives.

3.3 Product and Quotient Rule Fri Sept 25 Do Now Evaluate each 1) 2) 3)

3.3 Rules for Differentiation Colorado National Monument.

3.2 The Power Rule Thurs Oct 22 Do Now Find the derivative of:

HW # 41- Basic Exponents Worksheet Warm up Week 12, Day Three Evaluate b 2 for b = 4 4. n 2 r for n = 3 and r = 2.

3.4 Rates of Change Tues Sept 29 Do Now Find the derivative of each: 1) 2)

4.4 Concavity and Inflection Points Wed Oct 21 Do Now Find the 2nd derivative of each function 1) 2)

December 3, 2012 Quiz and Rates of Change Do Now: Let’s go over your HW HW2.2d Pg. 117 #

4.2 Critical Points Fri Dec 11 Do Now Find the derivative of each 1) 2)

3.8 Derivatives of Inverse Functions Fri Oct 30

position time position time tangent!  Derivatives are the slope of a function at a point  Slope of x vs. t  velocity - describes how position changes.

2.5 Evaluating Limits Algebraically Fri Sept 18 Do Now Evaluate the limits 1) 2)

3.6 Trigonometric Functions Wed Oct 21 Do Now Find the y’’ and y’’’ 1) 2)

4.1 Linear Approximations Thurs Jan 7

3.1 The Derivative Wed Oct 7 If f(x) = 2x^2 - 3, find the slope between the x values of 1 and 4.

MAT 1234 Calculus I Section 2.1 Part I Derivatives and Rates of Change

3.9 Exponential and Logarithmic Derivatives Mon Nov 9 Do Now Find the derivatives of: 1) 2)

Lesson 2.3 Product & Quotient Rules and Higher Derivatives.

4.9 Antiderivatives Tues Dec 1 Do Now If f ’(x) = x^2, find f(x)

5.6 Integration by Substitution Method (U-substitution) Fri Feb 5 Do Now Find the derivative of.

3.3 Product Rule Tues Oct 27 Do Now Evaluate each 1) 2)

Derivative Notation and Velocity. Notation for the Derivative.

Derivative Examples 2 Example 3

Ch. 8 – Applications of Definite Integrals 8.1 – Integral as Net Change.

HIGHER-ORDER DERIVATIVES Unit 3: Section 3 continued.

4.6 Curve Sketching Fri Oct 23 Do Now Find intervals of increase/decrease, local max and mins, intervals of concavity, and inflection points of.

3.8 Derivatives of Inverse Functions Wed Oct 5

PRODUCT & QUOTIENT RULES & HIGHER-ORDER DERIVATIVES (2.3)

DO NOW Find the derivative of each function below using either the product rule or the quotient rule. Do not simplify answers.

MTH1170 Higher Order Derivatives

2.1 Tangents & Velocities.

Motion Graphs Learning Target: Be able to relate position, velocity, and acceleration quantitatively and qualitatively.

3.6 Trigonometric Functions Tues Sept 27

Warm Up Identify the slope and y-intercept of each equation. Then graph. 1. Y = -5X X + 5Y = X = Y = 12.

3-2 The Derivative Wed Oct 5

Various Symbols for the Derivative

Unit 6 – Fundamentals of Calculus Section 6

Consider a car moving with a constant, rightward (+) velocity - say of +10 m/s. If the position-time data for such a car were.

SLOPE = = = The SLOPE of a line is There are four types of slopes

(This is the slope of our tangent line…)

A graphing calculator is required for some problems or parts of problems 2000.

2.3B Higher Derivatives.

2.1B Derivative Graphs & Differentiability

1. Find the derivative 2. Draw the graph of y’ from the graph of f(x)

32 – Applications of the Derivative No Calculator

Velocity-time graphs In this section you will

Describing Motion: Acceleration

Calculus I (MAT 145) Dr. Day Wednesday February 13, 2019

Warmup 1. What is the interval [a, b] where Rolle’s Theorem is applicable? 2. What is/are the c-values? [-3, 3]

TI-83: y = , 2nd x2 , 49 – x^2 to get Then hit graph Range [0, 7]

3.5 Limits at Infinity Horizontal Asymptote.

Presentation transcript:

3-5 Higher Derivatives Tues Oct 20 Do Now Find the velocity at t = 2 for each position function 1) 2)

HW Review: p.156 #

Higher Derivatives You can compute higher derivatives by continually taking derivatives of your answer Second derivative:

Ex 1 Calculate f’’’(-1) for

Ex 2 Calculate the first four derivatives of

Ex 3 If you use product rule for the first derivative, you will need it for any higher derivatives Ex: Find the first three derivatives of

Acceleration Since velocity is the first derivative of position, acceleration is the 2nd derivative Ex: A ball’s position can be modeled by the function Find the velocity and acceleration functions for the ball

Graph of the second derivative The graph of the second derivative describes how fast/slow the slope is changing Large second derivative = slope changes quickly

Closure Compute the fourth derivative of HW: p.163 #1-29 odds odds Quiz soon (Fri)