Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line. at (-2, -3)

Question

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line. ​  at (-2, -3)
​

Quizplus · Accepted Answer

We can use the formula for finding the slope of the tangent line:

f'(x) = lim h->0 [f(x+h) - f(x)]/h

A) f'(x) = 2x - 2, so f'(-2) = -6
The equation of the tangent line would be y = -6(x+2) - 3.

B) f'(x) = 3x^2 + 4x - 3, so f'(-2) = 2
The equation of the tangent line would be y = 2(x+2) - 3.

C) f'(x) = 2x - 1, so f'(-2) = -5
The equation of the tangent line would be y = -5(x+2) - 3.

D) f'(x) = 3x^2 + 6x - 5, so f'(-2) = 7
The equation of the tangent line would be y = 7(x+2) - 3.

Therefore, the best choice is B, because it gives us the slope 2, which is the only one that matches with point (-2,-3) in the given options.

Find the Slope of the Tangent Line to the Graph