Tangents & Normals

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

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?

• x=-1/3 or 1/2

• x= 1/3 or -1/2

• x=3 or -2

• x=-3 or 2

Tags

CCSS.HSF-IF.C.7D

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

•  $-\frac{3}{4}$  

•  $\frac{4}{3}$  

•  $\frac{3}{4}$  

•  $-\frac{4}{3}$  

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

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

The point on the curve y²=x at which the tangent is parallel to the line joining (1,4) and (3,2) is

• (5,6)

• (1/2,-1/2)

• (1/2,3/2)

• (-1/2,1/2)

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