Today in Calculus Go over homework Trig Review Mean Value Theorem

Slides:

Advertisements

Similar presentations

1 Local Extrema & Mean Value Theorem Local Extrema Rolle’s theorem: What goes up must come down Mean value theorem: Average velocity must be attained Some.

Advertisements

4.2 The Mean Value Theorem.

Warm up Problems 1. Find and classify all critical points of f (x) = 4x 3 – 9x 2 – 12x Find the absolute max./min. values of f (x) on the interval.

Differentiating the Inverse. Objectives Students will be able to Calculate the inverse of a function. Determine if a function has an inverse. Differentiate.

Squeeze Theorem & Intermediate Value Theorem

 Exploration:  Sketch a rectangular coordinate plane on a piece of paper.  Label the points (1, 3) and (5, 3).  Draw the graph of a differentiable.

Today in Calculus Go over homework Derivatives by limit definition Power rule and constant rules for derivatives Homework.

A car accelerates from a stop to 45 m/sec in 4 sec. Explain why the car must have been accelerating at exactly m/sec at some moment. 2 Do Now.

SECTION 4-4 A Second Fundamental Theorem of Calculus.

Jarrod Asuncion Period 1 Brose. Equation f(b) – f(a) = f’(c) b – a Slope = f’(c)

Rolle’s Theorem: Let f be a function that satisfies the following 3 hypotheses: 1.f is continuous on the closed interval [a,b]. 2.f is differentiable on.

Section 5.5 The Intermediate Value Theorem Rolle’s Theorem The Mean Value Theorem 3.6.

1 3.2 The Mean Value Theorem. 2 Rolle’s Theorem 3 Figure 1 shows the graphs of four such functions. Figure 1 (c) (b) (d) (a) Examples:

3.8 Derivatives of Inverse Functions Fri Oct 30

Calculus 3.1: Derivatives of Inverse Functions

If f (x) is continuous over [ a, b ] and differentiable in (a,b), then at some point, c, between a and b : Mean Value Theorem for Derivatives.

Calculus and Analytical Geometry Lecture # 15 MTH 104.

Section 3.2 Mean Value Theorem Math 1231: Single-Variable Calculus.

Algebra and Calculus 8-1 Copyright © Genetic Computer School 2007 Lesson 8 Fundamentals of Calculus.

MTH 252 Integral Calculus Chapter 6 – Integration Section 6.6 – The Fundamental Theorem of Calculus Copyright © 2005 by Ron Wallace, all rights reserved.

5.4 The Fundamental Theorem of Calculus. I. The Fundamental Theorem of Calculus Part I. A.) If f is a continuous function on [a, b], then the function.

3.8 Derivatives of Inverse Functions Wed Oct 5

3.8 Derivatives of Inverse Trig Functions

4.2 The Mean Value Theorem.

3.2 Rolle’s Theorem and the

4.2 The Mean Value Theorem State Standard

Lesson 63 Rolle’s Theorem and the Mean Value Theorem

Then  a # c in (a, b) such that f  (c) = 0.

Rolle’s Theorem Section 3.2.

Product and Quotient Rules

Inverse Trigonometric: Integration

5-2 mean value theorem.

3.3: Increasing/Decreasing Functions and the First Derivative Test

4.4 The Fundamental Theorem of Calculus

Local Extrema & Mean Value Theorem

Warm-Up: November 3, 2017 Find

Rolle’s Theorem and the Mean Value Theorem

6-4 Day 1 Fundamental Theorem of Calculus

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

Rolle’s Theorem.

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. {image}

§4.9 Antiderivatives There are two branches in calculus:

3.2 Rolle’s Theorem and the

Applications of Derivatives

Rolle’s Theorem.

Derivatives of Inverse Functions

AP Calculus November 9-10, 2016 Mrs. Agnew

AP Calculus AB Chapter 3, Section 1

4.3 – Derivatives and the shapes of curves

Increasing & Decreasing Functions First Derivative Test

3.2: Differentiability.

Derivatives of Inverse Functions

The Fundamental Theorem of Calculus

Section 4.2 Mean value theorem.

Differentiation Rules and Rates of Change

Sec 2.5: Continuity Continuous Function

Derivatives of Inverse Functions

Part (a) h(1) = f(g(1)) - 6 h(3) = f(g(3)) - 6 h(1) = f(2) - 6

Tangent Lines, Linear Approximations, & Theorems

The Intermediate Value Theorem

a) Find the local extrema

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

Rolle’s Theorem and the Mean Value Theorem

RAYAT SHIKSHAN SANSTHA’S S.M.JOSHI COLLEGE HADAPSAR, PUNE

Calculus Notes 4.2: The Mean Value Theorem.

3.2. Definition of Derivative.

Rayat Shikshan Sanstha’s S.M.Joshi College, Hadapsar -28

Section 4.2 Mean Value Theorem.

Sec 2.5: Continuity Continuous Function

Do Now: Find all extrema of

Presentation transcript:

Today in Calculus Go over homework Trig Review Mean Value Theorem

Inverse Trig Functions

Intermediate Value Theorem for Derivatives A function y = f ′(x) that is continuous on a closed interval [a, b] MUST take on every value between f ′(a) and f ′(b).

Mean Value Theorem (MVT) If f(x) is continuous at every point of the close interval [a,b] and differentiable at every point off its interior (a,b), then there MUST be at least one point c in (a,b) at which

Example Show f(x) = x2 satisfies the hypotheses of the MVT on the interval [0,3] and find each value c that satisfies the MVT.

Example Show satisfies the hypotheses of the MVT on the interval [0,9] and find each value c that satisfies the MVT.

Homework Finish worksheet