Derivatives and Equations of Tangent Lines!

Find the derivative of the function f(x) = 3x^2 - 2x + 5.

• f'(x) = 6x - 2.

• f'(x) = 3x^2 - 2

• f'(x) = 6x + 2

• f'(x) = 3x^2 - 2x + 5

Given the function f(x) = 2x^3 - 4x + 1, find the slope of the tangent line at the point (2, 5).

• The slope of the tangent line at the point (2, 5) is -5.

• The slope of the tangent line at the point (2, 5) is 20.

• The slope of the tangent line at the point (2, 5) is 10.

• The slope of the tangent line at the point (2, 5) is 0.

Calculate the derivative of the function h(x) = 5x^4 - 3x^2 + 2x - 1.

• h'(x) = 5x^3 - 3x + 2

• h'(x) = 10x^4 - 3x^2 + 2x - 1

• h'(x) = 20x^3 - 6x + 2.

• h'(x) = 20x^2 - 6x + 2

Solve for the equation of the tangent line to the function k(x) = x^2 + 3x - 2 at the point (1, 2).

• The equation of the tangent line is y = 4x - 2.

• The equation of the tangent line is y = 3x - 4.

• The equation of the tangent line is y = 2x - 1.

• The equation of the tangent line is y = 5x - 3.

Determine the slope of the tangent line to the function m(x) = 2x^2 - 6x + 4 at the point (3, 10).

• The slope of the tangent line to the function m(x) = 2x^2 - 6x + 4 at the point (3, 10) is 8

• The slope of the tangent line to the function m(x) = 2x^2 - 6x + 4 at the point (3, 10) is 6.

• The slope of the tangent line to the function m(x) = 2x^2 - 6x + 4 at the point (3, 10) is 3

• The slope of the tangent line to the function m(x) = 2x^2 - 6x + 4 at the point (3, 10) is -2

Given the function n(x) = 3x^3 - 2x^2 + 5x - 1, find the coordinates of the point where the tangent line is horizontal.

• The coordinates of the point where the tangent line is horizontal are (0, 1)

• The coordinates of the point where the tangent line is horizontal are (2, 3)

• The coordinates of the point where the tangent line is horizontal are (1, 5)

• The coordinates of the point where the tangent line is horizontal are (3, 7)

Find the derivative of the function p(x) = 4x^3 - 2x^2 + 3x - 1.

• 4x^3 - 2x^2 + 3

• 12x^3 - 2x^2 + 3

• 12x^2 - 4x + 3

• 4x^2 - 2x + 3

Identify the coordinates of the point where the tangent line to the function q(x) = x^2 - 4x + 3 is horizontal

• (1, 5)

• (2, -1)

• (0, 3)

• (3, 2)

Calculate the equation of the tangent line to the function r(x) = 2x^2 + 5x - 3 at the point (2, 7).

• The equation of the tangent line is y = 7x - 10.

• The equation of the tangent line is y = 2x + 5.

• The equation of the tangent line is y = 9x - 11.

• The equation of the tangent line is y = 3x - 1.

Find the equation of the tangent line of y = 2x^3+3x^2-12x+1 when x = -2

• y = x - 9

• y = x + 9

• y = 9

• y = -9