Calculus-Fall Review

Find the derivative of f(x) = 6x³⁰ -2x¹⁵ + 4x³ - 2x + 1

• f'(x) = 18x²⁹ + 30x¹⁵ + 12x³ 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² 
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² - 2
• f'(x) = 180x²⁹ - 30x¹⁴ + 12x² +1

If the position function for a particle is s(t) = -t² - t, what is the velocity function for the particle? 

• v(t) = -2
• v(t) -2t - 1 
• v(t) = t³
• v(t) = -t

Find the derivative f(x) = (x² + 2x)⁵

• f'(x) = 5(2x+2)⁴
• f'(x) = 5(x² + 2x)⁴
•  f'(x) = 5(x² + 2x)⁴(2x)
• f'(x) = 5(x² + 2x)⁴(2x + 2)

• Mean value theorem
• Rolle's theorem
• Intermediate Value Theorem
• Fundamental Theorem of Calculus

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

What is the limit?

• Infinity
• 20
• DNE
• 12

What is the limit?

• 5/2
• -2/3
• Infinity
• 17/3

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

• a
• b
• c
• d

What is the limit?

• DNE
• 6
• 0
• 12

• 1/2
• 0
• Infinity
• DNE