Given the function$\displaystyle f(x) = \frac{\ 2x}{x-4}$ , determine the coordinates of a point on f(x) where the slope of the tangent line equals the slope of the secant line that passes through A(5,10) and B(8,4)
Given the function$\displaystyle f(x) = \frac{\ 2x}{x-4}$ , determine the coordinates of a point on f(x) where the slope of the tangent line equals the slope of the secant line that passes through A(5,10) and B(8,4)
You need to find $\displaystyle \displaystyle \left(\frac{2x}{x-4}\right)'$ which is the gradient function of $\displaystyle \displaystyle \frac{2x}{x-4}$
$\displaystyle \displaystyle \left(\frac{2x}{x-4}\right)'= \left(\frac{2(x-4)-2x\times 1}{(x-4)^2}\right)$ via the quotient rule for differentiation.