Assistance solving calculus problem with solution written out

Question

Find a point x = c in the given interval at which the mean value theorem conclusion is true. Plot the secant line and the tangent line, showing that they really are parallel. g(x)=[(6)/(x )in the interval [1,4]]

Answer 1

I am going to assume you mean g(x)=6/x, for which the derivative is -6/x^2.

^{The slope of the secant is [3/2-5]/(4-1) = -3/2.}

-6/x² = -3/2 => x=2

If you have a graphing calculator (or you can use Desmos), you will see that the solution is correct. Of course, you will need to figure the equation of the tangent line and the secant to graph it!

However, if your notation in the problem submitted means something different, this solution will be of no value.