MATA33H3 Lecture Notes - Implicit Function, Farad
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next is on July 10 •
quiz starts thursday next week •
Test 2 Results
Avg - 72.77% •
Med - 77.5% •
90-100 17 •
80-89 28 •
70-79 20 •
60-69 23 •
50-59 10 •
<50 12 •
12.4 Implicit Differentiation
Motivation
The rate of change of
y with respect to x
For the rate of change at unless a specific point is specified or the system is sufficiently
simple, it is very hard to solve for y = f(x) explicitly
Remark
Explicit function 1.
position as a fact of time
2. Implicit function
conservation of energy
Idea
Given an equation of x,y
F(x,y) = 0 that defines y implicitly in terms of x, find , do
Differentiate both sides of the equation 1.
Solve for In terms of (x,y) 2.
Find 2. 3. 4. Find the equation 1.
of of the tangent line to y=f(x) at (3, 3)
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MATA33H3 Full Course Notes
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Document Summary
Next is on july 10 quiz starts thursday next week. F(x,y) = 0 position as a fact of time conservation of energy that defines y implicitly in terms of x, find , do. The rate of change of y with respect to x. For the rate of change at unless a specific point is specified or the system is sufficiently simple, it is very hard to solve for y = f(x) explicitly. Find the equation of of the tangent line to y=f(x) at (3, 3: find the equation of the tangent line of y as a function of x, defined implicitly as. Use implicit differentiation when looking for and y is given implicitly. B. y = (f(x)) y = product of many factors quotients of many terms. Suppose that you what to solve f(x) =0 f(x) = 1+x. Then if f is continuous [a,b] and f(a) & f(b) have opposite sign, then f(x)=0 has at least one solution in (a,b)
