Calculus 3.3 Review

Find the derivative of f(x)=(x³-2x)²

• 6x⁵ - 12x³+8x
• 6x⁵ - 16x³+8x
• x⁶-4x⁴+4x²
• 6x⁵ - 16x^3-8x

Find the derivative of g(x)=(3x-2)/(x²+2)

• 9x²+2
• 3(x²+2)/(x²+2)²
• (-3x²+4x +6)/(x²+2)²
• (-3x²+10)/(x²+2)²

Where is the graph neither continuous nor differentiable?

• x = -1, 0, 1, 2
• x = -1, 1
• x = -1, 0, 1
• x = -1, 0, 2

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

• a
• b
• c
• d

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

Tags

CCSS.8.EE.B.5

Set up the derivative of y=(3x⁴ - 7)*(5x² + 1)

• (12x³)*(10x)
• (3x⁴ - 7)*(10x) + (12x³)*(5x² + 1)
• (3x⁴ - 7)*(10x) - (12x³)*(5x² + 1)
• (3x⁴ - 7)/(10x) + (12x³)/(5x² + 1)

Which if the following is not a correct notation for 'derivative?'

• f'(x)
• y'
• dy
• dy/dx

Tags

CCSS.HSA.REI.A.1

Which of the following is the quotient rule for derivatives?

• h^'(x)=((g(x)f^'(x) + f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) - f(x)g(x)) / (g(x))

• h^'(x)=((g(x)f^'(x) - f(x)g^'(x)) / (g(x))²

• h^'(x)=((g^'(x)f^'(x) + f(x)g(x)) / (g(x))

Which of the following is the chain rule for derivatives utilizing the original function h(x) = f(g(x))

• h^'(x)=(f^'(g(x))(f^'(x))

• h^'(x)=(f^'(g(x))(g(x))

• h^'(x)=(f^'(g(x))(f(x))

• h^'(x)=(f^'(g(x))(g^'(x))

The acceleration function is the first derivative of...

• position

• velocity

• calculus

• particle motion