Differentiation Review

Find the derivative of f(x) = 5x² + 7x - 3.

• 2x + 7
• 10x + 7
• 10x + 4
• 2x + 4

Find the derivative of the given equation
f(x) = x⁴ + 4x³ - 2x²

• x³ + x² - x
• 4x³ + 12x² + 4x
• 4x + 12x - 4x
• 4x³ + 12x² - 4x

Tags

CCSS.HSA.APR.A.1

How many derivatives can you take of a function?

• only 3
• only 2
• only 1
• until you can no longer derive it

Tags

CCSS.HSF.IF.A.2

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

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

• The function is increasing
• The function is decreasing

The three situations where derivatives fail to exist are at corners or cusps, at a vertical tangent, and...

• horizontial tangent
• discontinuity
• curve
• intercepts

Differentiate f(x) = (9 - 4x²)^-1

• 8x/(9 - 4x²)^-2

• 8x/(9 - 4x²)²

• -8x/(9 - 4x²)^-2

• -8x(9 - 4x²)²

.

• Only the Chain Rule
• The quotient & the Chain Rules
• Only the Quotient Rule
• Product & Quotient Rules

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)

When do you use the chain rule?

• anytime you want
• when there is a function in a function
• where there are multiple layers to a lasagna (yum)
• when there is division