Review Midterm Calculus

If f(x)=(6x²-5x)⁷
what is f'(x)?

• 7(6x²-5x)⁶
• 7(6x²-5x)⁶⋅(12x)
• 7(6x²-5x)⁶⋅(12x-5)
• (12x-5)

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y

• moving left at a constant rate

• moving left and speeding up

• moving left and slowing down

• at rest

Tags

CCSS.HSA.SSE.A.1

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

when is the function f(x)=x²+6x+9 increasing?

• (3,∞)

• (-∞,3)

• (-3,-∞)

• (-3,∞)

Tags

CCSS.HSA.REI.D.10

what is the average rate of change of the function f(x)=x²-6x+6 from 2 to 6?

• 4

• 2

• 3

• 23/4

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t
What is the acceleration of the object at time t = 2 s?

• 64 m/s/s
• 60 m/s/s
• 66 m/s/s
• 70 m/s/s

At which x-value is f continuous but not differentiable?

• a
• b
• c
• d

Which of the following is needed when finding critical numbers?

• Take the derivative

• Take the integral

• Set the derivative = 0

• Consider when the derivative DNE

• Consider when the integral DNE

A particle's speed is decreasing if

• it's acceleration is positive
• it's velocity is positive
• it's velocity and acceleration have the same sign
• it's velocity and acceleration have different signs

Given the position function s(t) = - t³ + 26t² - 169t, determine if the particle is speeding up or slowing down when t = 2.

• Speeding up

• Slowing down