DL 2020: Tangent Lines and Implicit Diff.

the derivative is...

• slope of the secant line
• slope of the tangent line
• slope of the cosecant line
• slope of the normal line

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

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

Find the slope at x = 3 of the equation f(x) = 3x²

• 6x

• 27

• 18

• 3x

Tags

CCSS.8.EE.B.5

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.HSA.REI.C.7

CCSS.HSG.GPE.B.5

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

Find dy/dx by Implicit Differentiation 
x + 4y = 1

• -1/4
• -1 
• 4
• 1 

Find dy/dx by Implicit Differentiation 
x³ +y³  = 36

• 6 -x
• 3x² +3y² 
• −x²/y²
• 0

Find dy/dx
xy+y²=2

• -y/(x+2y)
• y/(x+2y)
• -3y/x
• -3x/y

find dy²/ d²x   of   x² + y² = 16
Make sure to go as far as you can!

• -16/ y³
• (y² - x ^dy/dx) /  (y³)
• (y² - x²) / y³