Unit 5 Analytics with derivatives-calculator active

The function f is defined by f(x) = 3x - 4cos(2x +1). What are all values of x that satisfy the Mean Value Theorem applied to the interval [-1 , 2] ?

• -0.692 and 1.263

• 0.285

• -0.479 and 1.049

• 0.517

• 1.578

• 2.5
• 6.25
• 14.4
• 6
• 5.75

Tags

CCSS.HSF.IF.B.6

• 4
• 2

Tags

CCSS.HSF.IF.B.6

The function f(x) is defined on the closed interval [0, 1] and satisfies f(0) = f (5) = f(1). On the open interval (0, 1),

f(x) is continuous and strictly increasing. Which of the following statements is true?

• f(x) attains a maximum value but not a minimum value on the closed interval [0, 1].

• f(x) attains a minimum value but not a maximum value on the closed interval [0, 1].

• f(x) attains both a minimum value and a maximum value on the closed interval [0, 1].

• F(x) is = 0 for all x.

• f(x) attains neither a minimum value nor a maximum value on the closed interval [0, 1].

• three

• one

• two

• four

• five

The function f is defined by f(x) = 3x - 4 cos (2x + 1). What are all

values of x that satisfy the conclusion of the Mean Value Theorem applied to f on the interval [-1, 2 ] ?

• -0.692

  and

  1.263

• -0.479

  and

  1.049

• 0.285

• 0.517

• 1.578

Let f be the function defined by f(x) = x + ln (x). What is the value of c for which the instantaneous rate of change

of f(x) at x = c is the same as the average rate of change of f(x) over [1,4] ?

• 0.456

• 1.244

• 2.164

• 2.342

• 2.452

• 1.123

• 0.543

• -1.123

• -0.543

• 2.456

• 0.1578

  and

  5.678

• 0.546

  and

  2.678

• 2.567

  and

  4.763

• 2.178

• 2.198

  and

  5.341

• 3.333

• 3.141

• 1.57

• 2.567

• 1.789