Normal and Tangent Lines

Find the slope of f(x) = -3x² – 6x at x = 1.

• m = 0

• f'(x) = -6x - 6

• f'(x) = 6x

• m = -12

Write the slope of the line tangent to the graph of y=x² – 2 at the point x = -8.

• 2

• -4

• -8

• -16

This is the equation of the line tangent to the graph of y=x²+3 at the point x = -1.

• y = -2x + 2

• y = 2x + 2

• -(1/2)x + (7/2)

• y = (1/2)x + (7/2)

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

Write the equation of the tangent line of the given equation through the point.

• y+2=9(x-3)

• y + 2 = 3(x-3)

• y - 2 = 3(x -3)

• y-2 = 9(x-3)

• 15x²

• (5/4)x⁴

• indeterminate

• ∞

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

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-7=-1/23 (x+1)
• y-7=-27(x+1)

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