Tangent and normal

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

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

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

•  $-\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{3}{4}$  

•  $-\frac{4}{3}$  

The slope of the normal to the curve $x=a\cos^3\theta,\ \ y=a\sin^3\theta$ at  $\theta=\frac{\pi}{4}$  is 

(a)  

The equations of all lines having slope 0 which are tangent to the curve $y=\frac{1}{x^2-2x+3}$  is

•  $y=1$  

•  $2y=1$  

•  $2y+1=0$  

•  $y+1=0$  

What is the equation of the line perpendicular to 5x+3y=0 and passing through the (-4, 6)?

• y-6=-5/3 (x+4)
• y-6=3/5 (x+4)
• y-6=5/3 (x+4)
• y-6= -3/5 (x+4)

What is the equation of the line normal to f(x)=5x⁵-2x  at x =-1?

• y+3 =23(x+1)
• y-3 = -1/23 (x-1)
• y+3 = -1/23 (x+1)
• 23y = -x-1

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

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

Tags

CCSS.HSF.IF.B.4