Finding Equations of Horizontal Tangent and Normal Lines

What are the two essential components needed to write the equation of any line?

• Two points

• Slope and a point

• Slope and y-intercept

• Derivative and integral

What is the y-coordinate of the point where the tangent line touches the curve at x=1 for the function f(x) = x^2 + 4x - 1?

• (1, 4)

• (1, 3)

• (1, 2)

• (1, 5)

Using the power rule, what is the derivative of x^3?

• 2x^2

• 3x^2

• x^2

• 4x^3

What is the slope of the tangent line at x=1 for the function f(x) = x^2 + 4x - 1?

• 7

• 6

• 5

• 4

How do you find the slope of the normal line if the slope of the tangent line is 2/3?

• 2/3

• -3/2

• 3/2

• -2/3

What is the equation of a horizontal line that is tangent to the curve at x=-2 for the function f(x) = x^2 + 4x - 5?

• y = -9

• y = -2

• y = -5

• y = -4

If a tangent line is parallel to the line 2x - y + 3 = 0, what is the slope of the tangent line?

• 1

• 4

• 2

• 3

For the function f(x) = 1/2 x^2 - 2x + 7, what is the y-coordinate when x=4?

• 7

• 5

• 6

• 8

What is the slope of the tangent line that is perpendicular to the line x + 4y - 8 = 0?

• -4

• -1/4

• 4

• 1/4

If the function f(x) = x^2 - kx is tangent to the line 4x - 5, what is the value of k?

• 2√5 + 4

• -2√5 + 4

• -2√5 - 4

• 2√5 - 4