Functions and Their Derivatives

Find f '(2)  if
f(x) = x² + 2x

• 2x + 2
• 6
• 12
• 2x

Tags

CCSS.HSF.IF.A.2

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

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

The derivative of a function is its

• Slope
• Maximum/Minimum
• Instantaneous rate of change
• Common Denominator

Find dy/dx for 
y = (x² + 1)³

• dy/dx = 3(x² + 1)²
• dy/dx = 3(2x)²
• dy/dx = 3(x² + 1)²(2x)
• dy/dx = 2x(x² + 1)²

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

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

Find the derivative: h(x)=(3x+2)(5x³+2x)

• 60x³+30x +12x-4
• 60x³-30x²+12x-4
• 45x³+30x²+12x+4
• 60x³+30x²+12x+4

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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