Concept explainers
In Exercises
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Calculus & Its Applications (14th Edition)
- bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.arrow_forwardDetermine whether each of the following statements is true or false, and explain why. The derivative of a sum is the sum of the derivatives.arrow_forwardRepeat the instruction of Exercise 11 for the function. f(x)=x3+x For part d, use i. a1=0.1 ii a1=0.1 11. Consider the function f(x)=4x2(1x) a. Find any equilibrium points where f(x)=x. b. Determine the derivative at each of the equilibrium points found in part a. c. What does the theorem on the Stability of Equilibrium points tell us about each of the equilibrium points found in part a? d. Find the next four iterations of the function for the following starting values. i. a1=0.4. ii. a2=0.7 e. Describe the behavior of successive iteration found in part d. f. Discuss how the behavior found in part d relates to the results from part c.arrow_forward
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