Maxima and Minima

What is the derivative of the function f(x) = 2x^5 + 7?

• 10x^4

• 5x^4

• 15x^4

• 8x^4

What is the second derivative of the function f(x) = 2x^3 - 6x^2 + 3?

• 6x - 6

• 12x - 6

• 6x^2 - 6

• 12x^2 - 6

What is the definition of absolute maxima of a function?

• The lowest point within a particular interval

• The lowest point within the entire domain

• The highest point within the entire domain

• The highest point within a particular interval

What is the definition of local minima of a function?

• The highest point within the entire domain

• The lowest point within the entire domain

• The highest point within a particular interval

• The lowest point within a particular interval

How can you find the maxima and minima of a function using graphs?

• By differentiating the function

• By drawing a diagram

• By solving word problems

• By finding critical points

What is the critical point of a function?

• A point where the derivative is 0

• A point where the function is undefined

• A point where the function is at a maximum

• A point where the function is at a minimum

In finding maxima and minima, what does it mean if the second derivative is negative?

• It is an absolute minimum

• It is an absolute maximum

• It is a relative minimum

• It is a relative maximum

What is the maximum value of the function y = 2x^3 - 3x^2 + 6?

• 2

• 1

• 0

• 3

What is the smallest value possible for the sum of the cube of one number and the square of the other if the sum of the two numbers is 2?

• 3

• 4

• 2

• 1

What is the derivative of the function f(x) = 13x^3 - 52x^2 + 4x?

• 39x^2 - 104x + 4

• 39x^2 - 52x + 4

• 39x^2 - 104x + 1

• 39x^2 - 52x + 1