2.1 - 2.2

The position function for a particular object is:

s(t) = -12t² + 51t + 26.

Which statement is true?

• The velocity is a constant.

• The initial position is 51.

• The velocity at time t = 1 is 27.

• The initial velocity is –24.

If f(x) = 2x² + 4, which of the following will calculate the derivative of f(x)?

• a

• b

• c

• d

Identify the f'(x) graph.

• a

• b

• c

• d

Find dy/dx: y = 4sinx – 5cosx + x

• 4cosx + 5sinx + 1

• -4cosx + 5sinx + 1

• 4cosx – 5sinx + 1

• 4cosx + 5sinx

A particle moves along the x-axis so that its position at time t is given by x(t) = t² -6t + 5. For what value of t is the velocity of the particle zero?

• 1

• 2

• 3

• 4

• ^-2π

• 1

• -1

• 2π

Let f and g be differentiable functions such that

f′(0)=3 and g′(0)=7.

If h(x)=3f(x)−2g(x)−5cosx−3, what is the value of h'(0)?

• -8

• -5

• 28

• 1

Let f be the function given by f(x)=5x³−3x−7.

What is the value of f′(−2) ?

• -114

• 57

• 50

• 17

The figure above shows the graph of a function f, which has a vertical tangent at x=2 and a horizontal tangent at x=4. Which of the following statements is false?

• f is not differentiable at x=−1 because the graph of f has a jump discontinuity at x=−1.

• f is not differentiable at x=2 because the graph of f has a vertical tangent at x=2.

• f is not differentiable at x=4 because the graph of f has a horizontal tangent at x=4.

• f is not differentiable at x=6 because the graph of f has a removable discontinuity at x=6.

• 0

• 1

• 1/2

• -1/2