Find an equation of the tangent line to the graph of the function at the given point.

Question

Find an equation of the tangent line to the graph of the function at the given point. ​   ​

Quizplus · Accepted Answer

The given point on the graph is (-2,-8) which lies on the graph of the function y = x^3 - 3x + 2. 
To find the equation of the tangent line at this point, we need to find the slope of the tangent. 
The slope of the tangent at any point on the graph of the function y = x^3 - 3x + 2 is given by the derivative of the function at that point. 
Hence, we find the derivative of the function y = x^3 - 3x + 2 as:
dy/dx = 3x^2 - 3
At the point (-2,-8), we have x=-2, hence the slope of the tangent at this point is:
dy/dx = 3(-2)^2 - 3 = 9
Therefore, the equation of the tangent line at the point (-2,-8) is given by: 
y - (-8) = 9(x - (-2))
Simplifying this, we get:
y = 9x + 10
Hence, the correct answer is A.

Find an Equation of the Tangent Line to the Graph