AIgo NotesQuiz for:
Applications of Derivatives - Rolle's & Mean Value Theorem, Concavity, Critical & Inflection Points,
Question 11
What is Newton's method used for?
A.Finding the area under a curve
B.Finding the slope of a curve
C.Approximating the zeros of a function
D.Finding the derivative of a function
Question 1
What is the formula for the average rate of change?
A.F(B) - F(A) / (B - A)
B.F(A) - F(B) / (A - B)
C.F(B) - F(A) / (A - B)
D.F(A) - F(B) / (B - A)
Question 2
What is the slope of the secant line?
A.Average rate of change
B.Instantaneous rate of change
C.Slope of the tangent line
D.Slope of the normal line
Question 3
What is the slope of the tangent line?
A.Average rate of change
B.Instantaneous rate of change
C.Slope of the secant line
D.Slope of the normal line
Question 4
What does the Mean Value Theorem state about the slope of the tangent line and the slope of the secant line?
A.They are always equal
B.They are never equal
C.They are equal at some point in the interval
D.They are equal at all points in the interval
Question 5
What are the conditions for Rolle's Theorem to apply?
A.Function is continuous and differentiable
B.Function is continuous on closed interval and differentiable on open interval
C.Function has equal values at endpoints
D.All of the above
Question 6
What is a critical point in calculus?
A.Where the function is at its highest point
B.Where the function is at its lowest point
C.Where the first derivative is zero or undefined
D.Where the second derivative is zero
Question 7
How can you determine if a function has a relative maximum at a point using the first derivative test?
A.First derivative is positive to the left and negative to the right
B.First derivative is negative to the left and positive to the right
C.First derivative is always positive
D.First derivative is always negative
Question 8
What does it mean if the function is concave up?
A.Second derivative is positive
B.Second derivative is negative
C.First derivative is increasing
D.First derivative is decreasing
Question 9
How can you determine if a function has a relative minimum at a point using the second derivative test?
A.First derivative is zero and second derivative is positive
B.First derivative is zero and second derivative is negative
C.First derivative is positive and second derivative is zero
D.First derivative is negative and second derivative is zero
Question 10
What is L'Hôpital's Rule used for?
A.Finding the slope of the tangent line
B.Evaluating limits of functions
C.Solving differential equations
D.Finding the derivative of a function
Question 11
What is Newton's method used for?
A.Finding the area under a curve
B.Finding the slope of a curve
C.Approximating the zeros of a function
D.Finding the derivative of a function
Question 1
What is the formula for the average rate of change?
A.F(B) - F(A) / (B - A)
B.F(A) - F(B) / (A - B)
C.F(B) - F(A) / (A - B)
D.F(A) - F(B) / (B - A)