Equations of Tangent & Normal Lines

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

• 6x

• 27

• 18

• 3x

Tags

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

What is the slope of the line normal to the curve y = x² + x at x = 1?

• -1

• -1/2

• -1/3

• -1/4

Tags

CCSS.HSG.GPE.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

What is the equation of the tangent line at x = 1  $of$   $f\left(x\right)=\ \sqrt{x}$  

•  $y=\frac{1}{2}x-\frac{1}{2}$  

•  $y=\frac{1}{2}x+\frac{1}{2}$  

•  $y=2x-1$  

•  $y=2x$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

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

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line

• a

• b

• c

• d

• e

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 the slope of the Normal line to: $f\left(x\right)\ =\ \frac{4\sqrt{x}}{5}$  
at x = 16

•  $\frac{2}{5}$  

•  $-\frac{1}{160}$  

•  $\frac{1}{10}$  

•  $-10$  

Tags

CCSS.HSG.GPE.B.5

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