5.3 The Derivative of an Inverse Function

Slides:

Advertisements

Similar presentations

Inverse Functions Section 1.8.

Advertisements

Inverse Functions © Christine Crisp.

6.4 Inverses of the Trigonometric Functions Jan 5 Do Now Solve for x 1)Sin x = -1/2 2)Tan x = 1.

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

 It must be one to one … pass the horizontal line test  Will a sine, cosine, or tangent function have an inverse?  Their inverses are defined over.

Derivative of an Inverse AB Free Response 3.

10.4A Polar Equations Rectangular: P (x, y) Polar: P (r,  )  r = radius (distance from origin)   = angle (radians)

Recall: These are equations of the form y=ab x-h +k, ones where the ‘x’ is in the exponent Recall: These are equations of the form y=ab x-h +k, ones where.

2.2 Basic Differentiation Rules and Rates of Change.

Warmup: 1). 3.8: Derivatives of Inverse Trig Functions.

3.9 Exponential and Logarithmic Derivatives Thurs Oct 8

I can solve one-step equations in one variable.. Equations that have the same solutions. In order to solve a one-step equation, you can use the properties.

Class Work Let’s start with some review!! 1.Solve for x. x 7 42 

4.4 The Fundamental Theorem of Calculus. Essential Question: How are the integral & the derivative related?

Unit 5C Day 2. Do Now  Let y = arccosu. Then u = ______.  Use this to derive dy / dx [arccosu].

3.8 Derivatives of Inverse Functions Fri Oct 30

Section 7.5 Trigonometric Equations Objective: To solve linear and quadratic trigonometric equations.

4.1 – ONE-TO-ONE FUNCTIONS; INVERSE FUNCTIONS Target Goals: 1.Obtain the graph of the inverse function 2.Determine the inverse of a function.

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

Blue part is out of 50 Green part is out of 50  Total of 100 points possible.

 I can… ◦ Find the inverse of a given relation or function.

Chapter 3: Transformations of Graphs and Data Lesson 8: Inverse Functions Mrs. Parziale.

Lesson 8 Chapter 2. Objectives Simplify expressions involving reciprocals.

Unit 1: Functions Minds On. Unit 1: Functions Lesson 5: Inverse Functions Example: Find the inverse of f(x) = (x – 3)

Finding Inverses of Equations Pg February 13, 2015.

2.5 Inverses Warm-up (IN) Learning Objective: to find the inverse of a relation or function and to determine whether the inverse of a function is a function.

5.3 Inverse Functions (Part I). Objectives Verify that one function is the inverse function of another function. Determine whether a function has an inverse.

3.8 Derivatives of Inverse Functions Wed Oct 5

One-to-One Functions A function is one-to-one if no two elements of A have the same image, or f(x1)  f(x2) when x1  x2. Or, if f(x1) = f(x2), then.

4-3 inviting inverses of trig deriv’s

AIM: How do we simplify, multiply and divide rational expressions?

Objectives: To find inverse functions graphically & algebraically.

2016 Derivatives of Inverse Trig Functions

Inverse Trigonometric: Integration

Find the derivative Find the second derivative

Learning Target: I will determine if a function is increasing or decreasing and find extrema using the first derivative. Section 3: Increasing & Decreasing.

Derivatives of inverse functions

3.1 Polynomial & Exponential Derivatives

Implicit Differentiation

TEMPERATURE CONVERSION

1-6 Real numbers and rational numbers

Inverse Linear Functions

3.6 Summary of Curve Sketching *pass out chart!

A. Symmetry with Respect to the Origin

Functions and Inverses

The Chain Rule Section 4 Notes.

Factor a difference of squares.

5.3 Inverse Function (part 2)

The General Power Formula

1.3 Find a Limit Algebraically

2.3B Higher Derivatives.

Inverse Function . Symbol f -1(x) means the. inverse of f(x) 

The Derivative of an Inverse Function

1.9 Inverse Functions f-1(x) Inverse functions have symmetry

10.2 Parametric Tangents & Areas

2.1B Derivative Graphs & Differentiability

Derivatives of Logarithmic Functions

INVERSE FUNCTIONS.

Inverse Functions Inverse Functions.

6-2: Inverse Functions and Relations

6.4 - Use Inverse Functions

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

Power Functions Investigating symmetry to determine if a power function is even, odd, or neither.

8. Derivatives of Inverse and Inverse Trig Functions

Use Inverse Functions Notes 6.4.

3.7-2 – Inverse Functions and Properties

Concavity & the 2nd Derivative Test

5.3 Inverse Function (part 2)

Presentation transcript:

5.3 The Derivative of an Inverse Function

Remember… If a function f has an inverse function f -1, Then f (a) = b implies that f -1(b) = a. x’s and y’s switch!

The Derivative of f -1(x): So…The derivative of the inverse is the reciprocal of the derivative of the original

Ex 1) Given that y = f(x) = x3 + 2x – 3 is a one-to–one function, and thus has an inverse, find (f -1)'(0).

Ex 2) Find , if: & .

5.6 The Derivative of Inverse Trig Functions

Ex 3) Find y:

Ex 4) Find y:

Ex 5) Find y:

HW – 5.3 pg. 349 # 71 – 75 odds, 95 5.6 pg. 378 # 41 – 49 odds, 61 & 63

Let g be the function which converts from Fahrenheit to Celsius. Ex 1) Let g be the function which converts from Fahrenheit to Celsius. Then g (F) = C = (5/9) (F – 32) Find g -1:

Ex 3) Find , if: , , & .