Calculus - Chapter 1-2

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in? (V = 4/3  $\pi r^3$  )

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

What is the derivative of tan x?

• sin x

• cos x

• sec x

• sec² x

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

• y+1=2(x+1)

• y=2x-1

• y=2x+2

• y= -x-1

Find the derivative
f(t) = (t² + 2t)⁵

• f'(t) = 5(2t+2)⁴
• f'(t) = 5(t² + 2t)⁴
•  f'(t) = 5(t² + 2t)⁴(2t)
• f'(t) = 5(t² + 2t)⁴(2t + 2)

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?  

• v = 0
• v = 1
• v = -1
• v = -2

Tags

CCSS.HSN.VM.A.3

What is f'(x) if f(x) = cos(5x⁴)?

• f'(x) = sin(20x³)
• f'(x) = 20x³ sin(5x⁴)
• f'(x) = -sin(20x³)
• f'(x) = -20x³ sin(5x⁴)

To find a function's horizontal tangent lines...

• Find f ' (0)

• Set f ' (x) = 0

• Set f(x) = 0

• Set f '' (x) = 0

To find the equation of a tangent line to a function you need...

• x and y intercepts of the function

• Slope (usually by taking derivative) and any point on the line

• Set the second derivative = 0.

• Slope (usually by taking derivative) and the point of tangency