Differentiate the function. {image}

Slides:



Advertisements
Similar presentations
The Chain Rule Section 3.6c.
Advertisements

C1: Tangents and Normals
The gradient as a normal vector. Consider z=f(x,y) and let F(x,y,z) = f(x,y)-z Let P=(x 0,y 0,z 0 ) be a point on the surface of F(x,y,z) Let C be any.
Rate of change / Differentiation (3)
Tangent Vectors and Normal Vectors. Definitions of Unit Tangent Vector.
Derivative Review Part 1 3.3,3.5,3.6,3.8,3.9. Find the derivative of the function p. 181 #1.
Question: Find the equation of a line that is parallel to the equation: 3x + 2y = 18.
Implicit Differentiation. Objectives Students will be able to Calculate derivative of function defined implicitly. Determine the slope of the tangent.
Chapter 14 Section 14.3 Curves. x y z To get the equation of the line we need to know two things, a direction vector d and a point on the line P. To find.
Tangents and Differentiation
In this section, we will consider the derivative function rather than just at a point. We also begin looking at some of the basic derivative rules.
Sec 15.6 Directional Derivatives and the Gradient Vector
Tangents. The slope of the secant line is given by The tangent line’s slope at point a is given by ax.
Find the slope of the line through P(-6,2) and Q(-5,3) m.
STROUD Worked examples and exercises are in the text PROGRAMME 8 DIFFERENTIATION APPLICATIONS 1.
Warm Up Determine a) ∞ b) 0 c) ½ d) 3/10 e) – Rates of Change and Tangent Lines.
SATMathVideos.Net If Line A passed through points (1,1) and (3,2). And Line B (not shown) is perpendicular to Line A. Which equation represents Line B?
Chapter 9 & 10 Differentiation Learning objectives: 123 DateEvidenceDateEvidenceDateEvidence Understand the term ‘derivative’ and how you can find gradients.
Chapter 5: Applications of the Derivative Chapter 4: Derivatives Chapter 5: Applications.
Calculus Continued Tangents and Normals Example Find the equations of the tangent and normal to the graph of at the point where.
Normal Vector. The vector Normal Vector Definition is a normal vector to the plane, that is to say, perpendicular to the plane. If P(x0, y0, z0) is a.
The gradient is 0.
Implicit Differentiation
Using The Discriminant
Find the equation of the tangent line to the curve y = 1 / x that is parallel to the secant line which runs through the points on the curve with x - coordinates.
DIFFERENTIATION APPLICATIONS 1
What is the average rate of change of the function f (x) = 8 x - 7 between x = 6 and x = 7? Select the correct answer:
Find the derivative of the vector function r(t) = {image}
Find the directional derivative of the function at the given point in the direction of the vector v. {image}
Find the domain of the function: {image} .
Sketch the region enclosed by {image} and {image}
Sketch the region enclosed by {image} and {image}
The Derivative and the Tangent Line Problems
Express the equation {image} in exponential form
©G Dear2008 – Not to be sold/Free to use
The gradient of a tangent to a curve
Solve the equation for x. {image}
Which of the following graphs is the graph of the derivative of the function {image} . 1. {applet}
(4, 0) (0, 4) (2, 0) (-4, 0) (0, -4) (0, 2) None of these choices
Literacy in Maths Gradient Tangent Normal
The graph of a function f(x) is given below
Use a table of values to estimate the value of the limit. {image}
Find 4 A + 2 B if {image} and {image} Select the correct answer.
Find an equation for the parabola, that has its vertex at the origin and directrix {image} Choose the correct answer from the following. y 2 = 2x y 2 =
Find the foci of the hyperbola 16 x y 2 = 400
List all possible rational zeros given by the rational zeros theorem (but don't check to see which actually are zeros). {image} Choose the answer.
Graph 2 Graph 4 Graph 3 Graph 1
Consider the function {image} and find the value of {image} Choose the correct answer from the following:
Solve the differential equation. {image}
Find an equation of the tangent to the curve at the point corresponding to the value of the parameter. {image} {image}
x = 4y - 4 x = 4y + 4 x = 4y - 1 y = 4x - 4 y = 4x - 1 y = 4x + 4
Indicate all x- and y-intercepts on the graph of the function y = x Choose the correct answer from the following: x-intercept (4,0), y-intercept.
Differentiate. f (x) = x 3e x
Problem: we can’t solve the differential equation!!!
For the function g(x) whose graph is given, which of the following numbers is greater? {image} or 0. {applet} {image}
Using the graph of f(x) below, estimate the value of the derivative at the point x = 0. {applet}
Find {image} by implicit differentiation:    {image} .
For the function g(x) whose graph is given, which of the following numbers is greater? {image} or 0. {applet} {image}
Use power series to solve the differential equation. y ' = 7xy
Determine the graph of the given function. {image}
Solve the equation: 6 x - 2 = 7 x + 7 Select the correct answer.
Find the directional derivative of the function at the given point in the direction of the vector v. {image}
If {image} , then if {image} exists, to what value does it converge
For the function f whose graph is given, state the limit
Warm-up: 1) Find the standard form of the equation of the parabola given: the vertex is (3, 1) and focus is (5, 1) 2) Graph a sketch of (x – 3)2 = 16y.
If {image} choose the graph of f'(x).
Sketch the curve. {image}
Which of the following expressions is the equation of the function {image} {applet}
The figure shows the graphs of {image} , {image} , {image}
Given that {image} {image} Evaluate the limit: {image} Choose the correct answer from the following:
Presentation transcript:

Differentiate the function. {image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The normal line to a curve C at a point P is, by definition, the line that passes through P and is perpendicular to the tangent line to C at P . Find an equation of the normal line to the parabola {image} at the point (2, - 1). Sketch the parabola and its normal line. Select the correct answer. 1. 2. {image} {applet} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50