advance function

Question

Determine the approximate slope of the tangent to the curve f(x)=3x+1/2x+7 at x=-2, to one decimal place.

Answer 1

To quickly find the slope of the tangent line for any differentiable function at any point, we will take the derivative of the function and plug in the given x value (-2 in this case) into the derivative to get our desired value.

So, if f(x) = (3x+1)/(2x+7), we must find f`(x). The quotient rule will work to give us the derivative. Once you find this derivative, plug in -2 for x and solve. The resulting number will be the slope of the tangent line of this curve at the point x=-2.