Calculus Concepts Quiz

• Quiz #3 covers multiple-choice questions related to calculus concepts.

Question 1

• The question asks to identify the FALSE statement among the given options.
• The exact change in y is f(x + Δx) - f(x).
• The differential of y is f'(x)(Δx).
• Linear approximation of y at x=c is f(c) + f'(c)(x - c).

Question 2

• The question asks to identify the TRUE statement among the given options.
• If f is continuous on a closed interval [a, b], then f can only have a maximum or a minimum at a time, not both extrema simultaneously.
• If f(x) has a horizontal tangent line at x = c, then (c, f(c)) is an inflection point of f(x).
• If f(x) = 3sin(x/2), then the maxima and minima have y-coordinates with an absolute value of 3.
• The tangent function has a repeating global maximum and global minimum.

Question 3

• The question asks to identify the TRUE statement among the given options.
• If (a, f(a)) is a critical point and f''(a) > 0, then (a, f(a)) is a local minimum.
• The function concaves upward at x=b when f''(b) > 0.
• If a parabola has an equation f(x) = x² + 2x + 1, then it will have a global minimum, but no absolute maximum.

Question 4

• Requires estimating the value of √4.4 using differentials.
• The answer options are 2.05, 2.1, 2.15, and 2.2.

Question 5

• The question is about the rate of change of the volume of a cone.
• Given volume V = (1/3)πr²h
• The options provide different expressions for dV/dt.

Question 6

• Concerns a hollow cylinder created by punching a hole through a solid cylinder.
• The solid cylinder has a radius of 5 cm and a height of 10 cm.
• The hole's radius is 0.3 cm smaller than the cylinder's radius.
• Requires estimating the volume of the hollow cylinder.

Question 7

• Given the function y = 5^(x²-2x+1)
• Tasked to find the slope at x = 2.
• The answer options involve natural logarithms 10, 10ln5 or ln5.