Suppose the function
f(x) = 3 × 2x − 2.25x
describes a physical situation that makes sense only for whole numbers between 0 and 15. For what value of x does f reach a maximum, and what is that maximum value? (Suggestion: We suggest beginning with a table starting at 0 with a table increment of 1 and then panning further down the table. Round your answer for the maximum value to two decimal places.)
x-value | |
maximum value of f |
Suppose the function f(x) = 3 × 2x − 2.25x describes a physical situation that makes...
Previous Answers 12 points CraudColAlg5 2AFL3.007 My Notes Ask Your Teacher The following illustrates an application of optimization using parabolas. A study found that the cost C per pupil of operating a high school in a certain country depends on the number n of students enrolled. The cost is given by C=65,000-500n+ n? oolars per pupi What enrollment produces the minimum cost per pupil? n250 students What is the minimum cost? 25000 Need Help? Read Talk to a Tutor I...
x+3 2x Define f(x) for all real numbers x = 0. Is f a one-to-one function? Prove or give a counterexample. (Note that the write-up of the proof or counterexample should only have a few of sentences.) If the co-domain is all real numbers not equal to 1, is f an onto function? Why or why not? (Note this problem does not require a full proof or formal counterexample, just an explanation.)
Suppose that f(x) is a differentiable function such that the tangent line at x = 3 is given by y=-***. How many of the following statements MUST be true? I. According to the linearization of fat x = 3. f3.001) - 0.9989 IL (3) -0. III. f is concave down on an open interval containing x = 3. IV. The graph of y = f(x) attains a maximum value on the interval (-1,4). V. Applying Newton's Method to approximate the...
Consider the function f(x) = 2x + 6x2 - 144x + 6. For the following questions, write inf for 0, -inf for --O, U for the union symbol, and NA (ie. not applicable) if no such answer exists. a.) f'(x) = 6x^2+12X-144 b.) f(x) is increasing on the interval(s) c.) f(x) is decreasing on the interval(s) d.)f(x) has a local minimum at NA e.)f(x) has a local maximum at NA f.)f"(x) = 12x+12 g.)f(x) is concave up on the interval(s)...
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Find the absolute maximum and minimum of the function f(x,y)=2x? - 8x + y2 - 8y + 7 on the closed triangular plate bounded by the lines x = 0, y = 4, and y = 2x in the first quadrant. On the given domain, the function's absolute maximum is The function assumes this value at . (Type an ordered pair. Use a comma to separate answers as needed.) On the given domain, the function's absolute minimum is The function...
3. For the function f(x) --2x, do the following: (a) Complete a table of values containing at least five points. (b) Sketch the function on the coordinate plane. (c) Describe the function's end behavior. Answer 2 0 2 f(x) f(x) 36 28 20 12 0 -2-4 12 20 (c) End behavior:
Find the absolute maximum value on (0.00) for f(x) = 4x - 2x In x Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice O A. The absolute maximum is at x = (Round to two decimal places as needed.) OB. There is no absolute maximum. Describe the graph off at the given point relative to the existence of a local maximum or minimum. Assume that f(x) is continuous on (-2,00). (9.f(9))...
3. Suppose f : [0,) + R is a continuous function and that L limf(x) exists is a real number). Prove that f is uniformly continuous on (0,.). Suggestion: Let e > 0. Write out what the condition L = lim,+ f(t) means for this e: there erists M > 0 such that... Also write out what you are trying to prove about this e in this problem. Note that f is uniformly continuous on (0.M +1] because this is...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...