For Exercises 69–84, draw a graph to match the description given. Answers will vary.
has a negative derivative over
and
and a positive derivative over
and
Want to see the full answer?
Check out a sample textbook solutionChapter 2 Solutions
Calculus and Its Applications (11th Edition)
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Each of Exercises 25–36 gives a formula for a function y = f(x). In each case, find f-x) and identify the domain and range of f-. As a check, show that f(fx)) = f-"f(x)) = x. 25. f(x) = x 26. f(x) = x, x20 %3D %3D 27. f(x) = x + 1 28. f(x) = (1/2)x – 7/2 30. f(x) = 1/r, x * 0 %3D 29. f(x) = 1/x, x>0 x + 3 31. f(x) 32. f(x) = VE - 3 34. f(x) = (2x + 1)/5 2 33. f(x) = x - 2r, xs1 (Hint: Complete the square.) * + b x - 2' 35. f(x) = b>-2 and constant 36. f(x) = x? 2bx, b> 0 and constant, xsbarrow_forwardSection 11.6: Calculus of Vector-Valued Functions - #39arrow_forwardIn Exercises 27–58, find the critical points and the intervals on which the function is increasing or decreasing. Use the First Derivative Test to determine whether the critical point yields a local min or max (or neither).arrow_forward
- In Exercises 25–30, give a formula for the extended function that iscontinuous at the indicated point.arrow_forward10 helparrow_forwardIn Exercises 6–10, let f(x) = cos x, g(x) = Vx+ 2, and h(x) = 3x?. Write the given function as a composite of two or more of f, g, and h. For example, cos 3x? is f(h(x)). 6. V cos x + 2 1. V3 cos?x + 2 8. 3 cos x + 6 ). cos 27x* 10. cos V2 + 3x²,arrow_forward
- Classify the quadratic forms in Exercises 9–18. Then make a change of variable, x = Py, that transforms the quadratic form into one with no cross-product term. Write the new quadratic form. Construct P using the methods of Section 7.1. 11. 2x² + 10x1x2 + 2x3arrow_forward#4 (2)arrow_forwardFind the natural spline for the data: x0 = 0, x1 = 1, x2 = 2, and f(x0) =1.2, f(x1) = 1.3, f(x2) = 1.0.arrow_forward
- Select the function that is O(2n)?arrow_forwardThe population of a small village grows exponentially. At time t the number N(t) of people in the village is given by the formula N(t) = Noet where No represents the initial size of the population and r is the relative rate of growth. Suppose the population increases from 800 to 1200 over a period of 4 years.arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage