All Educational Materials for ENG210Y1 at University of Toronto St. George (UTSG)

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MAT135H1 Lecture Notes - Lecture 6: Function Composition

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22 Sep 2020
Composite function: given two functions f x and ( )g x , a composite function is defined as: f glad of gcfcx. Example 1: given f x x= and g x x= + , de
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MAT135H1 Lecture Notes - Lecture 3: If And Only If

3 Page
22 Sep 2020
2. 2 derivatives of polynomial functions: constant function rule: k= , where k" is a constant, then _________________________ f"cx o. Example 1: find t
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MAT135H1 Lecture 1: 4.1 Increasing and Decreasing Functions

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22 Sep 2020
2 f x is decreasing (falls) on an interval if, x for any value of 1 x< , determine the intervals where f x is increasing and decreasing increasing when
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MAT135H1 Lecture Notes - Lecture 3: Inflection, If And Only If

3 Page
22 Sep 2020
4. 4 concavity and points of inflection: a function, a function f x is concave up on an interval if, the graph of the function is above the tangent on
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MAT135H1 Lecture Notes - Lecture 2: Maxima And Minima

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22 Sep 2020
4. 2 critical points, local maxima, and local minima: recall from chapter 3, when we set f x = and solve for x", we determine critical points which cou
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MAT135H1 Lecture 10: 3.4 Optimization in Economics and Science (3)

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22 Sep 2020
In business, optimization involves maximizing profits and minimizing costs. Revenue = (price per unit) x (number of units sold) Example 1: a commuter t
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MAT135H1 Lecture 9: 3.3 Optimization Problems (3)

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22 Sep 2020
3. 3 optimization problems: optimization is a procedure used in many fields to determine the best possible solution given a set of restrictions. [ex. d
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MAT135H1 Lecture Notes - Lecture 2: Ath

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22 Sep 2020
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MAT135H1 Lecture 8: 3.2 Max and Min Values on an Interval

3 Page
22 Sep 2020
For f x on an interval [a, b: find the derivative, find all points in the interval [a, b] where, evaluate, compare the value is step 3: x f f. 0 x = f
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MAT135H1 Lecture Notes - Lecture 4: If And Only If, Product Rule

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22 Sep 2020
2. 3 the product rule: product rule, when given the product of two functions, p x f x g x. , then p x f x og x t f x g1cx. Leibniz notation: if u" and
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