Equations of Tangents and Normals

The normal to the curve is 

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

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

•  $-\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{3}{4}$  

•  $-\frac{4}{3}$  

Write the equation of the normal line of:  $f\left(x\right)=2x^2-\frac{1}{x}$  at x = 1

•  $y=-\frac{1}{5}x+\frac{4}{5}$  

•  $y=5x-6$  

•  $y-1=5\left(x-1\right)$  

•  $y-1=-\frac{1}{5}\left(x-1\right)$  

Tags

CCSS.HSG.GPE.B.5

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

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

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

Tags

CCSS.HSG.GPE.B.5

CCSS.HSA.REI.C.7

Find the equation of the tangent line at the point (-1,1) of: $f\left(x\right)\ =\ x^4$  

•  $y=-\frac{1}{4}x-3$  

•  $y=-4x-3$  

•  $y=\frac{1}{4}x+3$  

•  $y=4x+3$  

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The equation of the normal to the curve $y=x^4–\ 6x^3+13x^2\ –\ 10x+5$  at  $\left(0,\ 5\right)$  is

•  $x\ \ +10y+50=0$  

•  $x\ –\ 10y+50=0$  

•  $x\ –\ 10y-50=0$  

•  $x\ +10y+50=0$  

Find the equation of the normal line at (3,5) of

 $y=x^2-3x+5$  

•  $y-5=3\left(x-3\right)$  

•  $y-5=\frac{1}{3}\left(x-3\right)$  

•  $y-5=-\frac{1}{3}\left(x-3\right)$  

•  $y-3=\frac{1}{3}\left(x-5\right)$