1. Create your own function f(x) of the form F (x) = f (x)·g (x). In other words, F(x) is a product of two different functions. For example F (x) = x²e" or F (x) = xsin (2x). Make sure that the function you created can be differentiated using the product rule and cannot be simplified to a single function. 2. Using your function in (1), solve its first derivative analytically.
1. Create your own function f(x) of the form F (x) = f (x)·g (x). In other words, F(x) is a product of two different functions. For example F (x) = x²e" or F (x) = xsin (2x). Make sure that the function you created can be differentiated using the product rule and cannot be simplified to a single function. 2. Using your function in (1), solve its first derivative analytically.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Transcribed Image Text:1. Create your own function f(x) of the form F (x) = f (x)· g (x). In other words, F(x) is a product of two different functions. For example F (x) = x² e"
or F (x) = xsin (2x). Make sure that the function you created can be differentiated using the product rule and cannot be simplified to a single function.
2. Using your function in (1), solve its first derivative analytically.
3. Solve the first derivative of F(x) using forward, backward and centered difference approaches. Which of the three approaches gives the most accurate
value? Explain your answer.
4. Is it possible to get the exact value of the definite integral of a function using Trapezoidal Rule and Simpson's 1/3 Rule? If yes, in what case will these
rules give us the exact values of the definite integral? Give a specific example for each rule.
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