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Using the Mean Value Theorem In Exercises 37–46, determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the Mean Value Theorem can be applied, find all values of c in the open interval (a, b) such that
If the Mean Value Theorem cannot be applied, explain why not.
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Calculus
- In Exercises 15–22, calculate the approximation for the given function and interval.arrow_forwardIn Exercises 83–86, determine whether thestatement is true or false. If it is false, explain why or give anexample that shows it is false. If the graph of a function has three x-intercepts, then it musthave at least two points at which its tangent line is horizontalarrow_forwardIn Exercises 17–20, the linear function. use the limit definition to calculate the derivative ofarrow_forward
- In Exercises 83–85, you will use a CAS to help find the absolute extrema of the given function over the specified closed interval. Per-form the following steps. a. Plot the function over the interval to see its general behavior there. b. Find the interior points where ƒ′ = 0. (In some exercises, you may have to use the numerical equation solver to ap-proximate a solution.) You may want to plot ƒ′ as well. c. Find the interior points where ƒ′ does not exist. d. Evaluate the function at all points found in parts (b) and (c) and at the endpoints of the interval. e. Find the function’s absolute extreme values on the interval and identify where they occur. 83. ƒ(x) = x4 - 8x2 + 4x + 2, [-20/25, 64/25] 84. ƒ(x) = -x4 + 4x3 - 4x + 1, [-3/4, 3] 85. ƒ(x) = x^(2/3)(3 - x), [-2, 2]arrow_forwardIn Exercises15–36, find the points of inflection and discuss theconcavity of the graph of the function. f(x)=\frac{6-x}{\sqrt{x}}arrow_forwardIn Exercises 51–54, graph the function ƒ to see whether it appears to have a continuous extension to the origin. If it does, use Trace and Zoom to find a good candidate for the extended function’s value at x = 0. If the function does not appear to have a continuous extension, can it be extended to be continuous at the origin from the right or from the left? If so, what do you think the extended function’s value(s) should be?arrow_forward
- In Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. x2 – 25 = x - 5 5 139. X - x? + 7 140. = x? + 1 7 7 domain of f(x) = is x(x – 3) + 5(x - 3) 141. The (-0, 3) U (3, 0). 142. The restrictions on the values of x when performing the division f(x) h(x) g(x) k (x) are g(x) + 0, k(x) # 0, and h(x) + 0.arrow_forwardIn Exercises 25–30, give a formula for the extended function that iscontinuous at the indicated point.arrow_forwardUse Definition 0.10 to show that each pair of functions in Exercises 67–70 are inverses of each other. 1 2 67. f(x) =2 – 3x and g(x) = -x+ 3 68. f(x) = x² restricted to [0, 0) and g(x) = V 69. f(x) = and g(x) = 1+x 1-x 1 1 70. f(x) = and g(x) 2x 2xarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage