Reference no: EM131019965
1. The function f(x)=x4 - 4x3 + 8x has a critical point at x=1. Use the second derivative test to identify it as a local maximum, a local minimum or neither.
Using calc or computer, graph the following functions. Describe briefly in words the interesting features of the graph including the locations of the critical points and where the function is increasing/decreasing. Then use the derivative and algebra to explain the shape of the graph.
2. Solve the following and show work.
i. f(x)=x3-6x+1
ii. f(x)=3x5-5x3
3. How many real roots does the equation x5 + x + 7 = 0 have? How do you know?
Use the first derivative to find all critical points and use the second derivative to find all inflections points. Use a graph to identify each critical point as a local maximum, a local minimum or neither.
4. Solve the following, show work.
f(x) = x4 - 8x2 + 5
5. For f(x) = x3 - 18x2 - 10x + 6, find the inflection point algebraically. Graph the function with a calculator or computer and confirm your answer.
6. When I woke up this morning I put on a light jacket, although the temperature was dropping because it seemed the temperature would not go much lower. I was wrong. Around noon a northerly wind blew up and the temp began to drop faster and faster. The worst occurred around 6pm when it started rising again.
a) when was there a critical point in the graph of temperature as a function of time?
b) When was there an inflection point in the graph of temperature as a function of time?
Create a graph of a function on the interval 0 ≤ x ≤ 10 with the following given properties.
7. Has a local minimum at x=3, local maximum x=8 but global maximum and global minimum at the end points of the interval.
8. Has local and global minimum at x=3, local and global minimum at x=8.
9. Plot the graph of f(x)=x3-ex using a calculator or computer to find all local and global maxima and minima for:
a) 1 ≤ x ≤ 4
b) -3 ≤ x ≤ 2
10. For f(x)=x - ln x, and 0.1 ≤ x ≤ 2, find the values of x for which:
a) f(x) has a local maximum or local minimum. Indicate which ones are maxima and which are minima.
b) F(x) has a global maximum or minimum
11. During a flu outbreak in a school of 763 children, the number of infected children, I, was expressed in the terms of susceptible (but still healthy) children. S, by the expression I = 192ln(S/762)-S+763
What is the maximum possible number of infected children?
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Summer circuit using an ideal op amp
: A weighted summer circuit using an ideal op amp has three inputs using 10-kΩ resistors and a feedback resistor of 50 kΩ. A signal v1 is connected to two of the inputs while a signal v2 is connected to the third. Express vO in terms of v1 and v2. I..
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What is the maximum value
: For the smallest resistance in the circuit, use 500Ω. If the op amp saturates at±10 V, what is the maximum value that RL can have while the current source supplying it operates properly?
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Give the lower riemann sum of f over the given interval
: Graph the function f(x) = -|x| + 4 over the interval [-2,1]. Give the lower Riemann sum of f over this interval with respect to the partition- P = {-2, 0, 1}.
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Design a miller integrator
: Design a Miller integrator that has a unity-gain frequency of 10 krad/s and an input resistance of 100 k_. Sketch the output you would expect for the situation in which, with output initially at 0 V, a 2-V, 100-μs pulse is applied to the input. Ch..
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What is the maximum possible number of infected
: During a flu outbreak in a school of 763 children, the number of infected children, I, was expressed in the terms of susceptible (but still healthy) children. What is the maximum possible number of infected?
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What temperature would you expect rotational heat capacity
: At approximately what temperature would you expect the rotational heat capacity of a gas of HD molecules to "freeze out," that is, to fall significantly below the constant value predicted by the equipartition theorem?
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Problem regarding the instrumentation amplifier
: Consider the instrumentation amplifier of Fig. 2.20(b) with a common-mode input voltage of +3 V (dc) and a differential input signal of 100-mV peak sine wave. Let 2R1 = 2 kΩ, R2 = 50 k Ω, R3 = R4 = 10 kΩ. Find the voltage at every node in the circ..
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Effect of resistor tolerances on ad
: For the difference amplifier shown in Fig. P2.62, let all the resistors be 10 kΩ± x%. Find an expression for theworst-case common-mode gain that results. Evaluate this for x = 0.1, 1, and 5. Also, evaluate the resulting CMRR in each case. Neglect ..
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Why has there been an increase in the research on asl
: Explain Deaf epistemologies and what must be included for Deaf and Hard of Hearing students to suceed in the educational setting.
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