tangents and normals

What is the equation of the horizontal line through (-3, 6)?

• x=-3
• y=6
• x=6
• y=-3

What is the equation of the vertical line through (8, -4)?

• x=8
• y=8
• x=-4
• y=-4

Which of the following means "first derivative"

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

Tags

CCSS.HSF.LE.B.5

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

• y+1=2(x+1)
• y = 2x - 1
• y=2x+2
• y = 2x -3

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

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

Write the slope of the line tangent to the graph of y=x² – 2 at the point x = -8.

• 2

• -4

• -8

• -16

If f '(x) = 0, what does that mean with respect to the tangent line?

• Tangent line is vertical

• Tangent line has a positive slope

• Tangent line is horizontal

• Tangent line has a negative slope

Tags

CCSS.HSF.IF.B.4

The normal to the curve is 

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

For what value(s) of x does the function

f(x) = 4x³- x²- 2x+5 have a horizontal tangent? *Hint: use your GDC...

• x=-1/3 or 1/2

• x= 1/3 or -1/2

• x=3 or -2

• x=-3 or 2

If the gradient of the tangent is  $\frac{4}{3}$  , what is the gradient of the normal at the same point?

•  $-\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{3}{4}$  

•  $-\frac{4}{3}$