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Question: Let ƒ: R → R be a differentiable function on an interval I. Show that
(i) if ƒ'(x) = 0 for each x e I, then ƒ is constant on the interval.
(ii) if ƒ'(x) > 0 on (a, b), then ƒ is strictly increasing on (a, b).
two pain relief drugs are being considered. a random sample of 8 doses of the first drug showed that the average amount
The expenditure of a household on consumer goods, C, is related to the household's income, y, in the following way: When the household's income is $1000.
EXPECTED HOME SALES Sally Leonard, a real estate broker, is relocating in a large metropolitan area where she has received job offers from realty company A.
Let V and W be the subspaces of R^2 spanned by (1,1) and (1,2), respectively. Find vectors v ∈ Vand w ∈ W so v + w = (2, -1).
Solve the BVP for the beam where the force is given by f(x) = cos x and the beam is L = π units in length. Determine the location(s) throughout the beam where the deflection is the largest.
The points (4, 1, 7) and (10,9,7) are endpoints of a diameter of a sphere. How to find the center and radius of the sphere?
Suppose you have 3 nickels, 2 dimes, and 6 quarters in your pocket. If you draw a coin randomly from your pocket, what is the probability that
Suppose you have two functions f and g and you use them to form a composite function. Under what conditions will they be the same? Include a numerical example in your answer.
if the price elasticity of demand for cigarette is -0.03 then find the percentage in the quantity demanded when the price increases by 10 percent?
Find the area of a sector having a central angle of 60° in a circle of radius 8 inches. Find the perimeter and area of a circular sector whose angle is 3.5 radians if the circumference of the circle is 58 ft.
On the graph of y = sin x in Fig., draw tangent lines at the indicated points and determine the slopes of these tangent lines.
Estimate and plot the uncertainty in the temperature measurement as a function of the temperature of the sphere.
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