Assignment:
Q1. Find the Max and Min. values attained by the function
h(x) = x - 1/x + 1
on the interval [0,2]
Q2. A mass of clay with a volume
432in3
is formed into two cubes. What is the minimum possible total surface area of the two cubes? What is the Max?
Q3. f(x) = x3 - 3x +1
The equation has 3 distinct real roots. Approximate their locations by evaluating f at -2,-1, 0, 1, and 2. Then use Newton’s method to approximate each of the 3 roots to four-place accuracy.
Q4. Sand falling from a hopper at
10πFT3/sec
forms a conical sand pile whose radius is always equal to its height. How fast is the radius increasing when the radius is 5ft?
Q5.f(x) = x2/ x - 1
Find the open intervals on the x-axis on which the function is increasing and those on which it is decreasing.
Q6. 600πIN2
What is the maximum possible volume of a right circular cylinder with a total surface area (including the top and the bottom)?
Q7. Find the interval on which the function
f(x) = (x - 2)2 (x + 3)2
is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.
Q8. Find the exact coordinates of the inflection points and critical points of the function
f(x) = 2x3 + 3x2 -180x + 150
on the interval (-10, 10)
Q9. Graph f(x). Identify all extrema, inflection points, intercepts, and asymptotes. Show the concave structure clearly and note any discontinuities.
f(x) = x2/ x- 1
Provide complete and step by step solution for the question and show calculations and use formulas.