Question

The local linear approximation to the function g at x=−3 is given by y=4x−7. What is the slope of the tangent line at x=−3?

a) 4
b) -3
c) 7
d) Cannot be determined

Answer 1

The slope of the tangent line to the function g at x=-3 is the coefficient of x in the equation y=4x-7, which is 4, corresponding to option a.

Step-by-step explanation:

The slope of the tangent line to the function g at x=-3 is the coefficient of x in the equation y=4x-7, which is 4, corresponding to option a.

The question requires us to find the slope of the tangent line to the function g at x=-3. It is given that the local linear approximation of g at x=-3 is y=4x-7. This approximation is actually the equation of the tangent line at the point of tangency.

By definition, the slope of the tangent line is the coefficient of x in this linear approximation, which is also the derivative of the function g at the point x=-3. Therefore, the slope of the tangent line at x=-3 is 4, which corresponds to option a among the provided choices.