# Friday March 2 2018 MAT 146 Friday March

- Slides: 20

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

Friday, March 2, 2018 MAT 146

(A) What Does it Mean for Something to be a Solution to an Equation? (i) Is x = − 1/5 a solution to the equation 4 x + 7 = 2 x – 3 ? (ii) State all solutions to the equation x 2 – x = 12. (iii) Is x = 4 a solution to the equation 3 ex = 12 ? (B) What Information About a Function is Revealed Through Its First Derivative? g’(x) = – 8 – 6 x 2. Gordon looked at the derivative of g(x) and shouted, “The function g is always decreasing!” How did he know? Friday, March 2, 2018 MAT 146

Differential Equation • A differential equation is an equation that contains one or more derivatives. • Here’s a differential equation you have already solved: y’ = 2 x What is the solution of this differential equation? Friday, March 2, 2018 MAT 146

Solution • A general solution to a differential equation is a family of functions that satisfies a given differential equation. • A particular solution to a differential equation (also called the solution to an initial-value problem) is a particular function that satisfies both a given differential equation and some specified ordered pair for the function. Friday, March 2, 2018 MAT 146

DE Questions y’ + 2 y = 2 ex Friday, March 2, 2018 MAT 146

DE Questions growing diminishing equilibrium values Friday, March 2, 2018 MAT 146

DE Questions Friday, March 2, 2018 MAT 146

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