Equations of the Tangent Line

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

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

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

• 6x

• 27

• 18

• 3x

• a

• b

• c

• d

• e

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

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.

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.

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.

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