Derivatives, Tangent, and Normal Lines

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

• 2x + 7
• 10x + 7
• 10x + 4
• 2x + 4

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

Differentiate f(x) = (9 - 4x²)^-1

• 8x/(9 - 4x²)^-2

• 8x/(9 - 4x²)²

• -8x/(9 - 4x²)^-2

• -8x(9 - 4x²)²

Find an equation of the tangent line to the graph of f(x) at the point (1, 100)
f(x) = (5x⁵ + 5)²

• y = 500x + 400
• y = 100x + 400
• y = -500 x - 400
• y = 500x - 400

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the derivative of this function

• (8x³ -60x/(2x²-5)²
• 16x⁴/(2x²-5)²
• (8x⁴ -60x²)/(2x²-5)²
• 3x/(2x²-5)²

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Derivative means the same thing as

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

Tags

CCSS.HSS.ID.C.7

How do you find horizontal tangent lines?

• Find where the derivative is undefined
• Find where the derivative equals zero
• Find where the derivative is 1
• Find where the derivative is negative

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

Which of the following means "first derivative"

• f'(x)
• y'
• dy/dx
• all of the above

Tags

CCSS.HSF.LE.B.5

The normal to the curve is 

• the derivative
• the integral
• perpendicular to the tangent  to the curve
• the tangent to the curve

Tags

CCSS.HSG.CO.A.1

CCSS.HSG.GPE.B.5