The function is written as: f(x) = log(-20x + 12√x) To find the maximum value, differentiate the equation in terms of x, then equate it to zero. The solution is as follows.
The formula for differentiation would be: d(log u)/dx = du/u ln(10) Thus, d/dx = (-20 + 6/√x)/(-20x + 12√x)(ln 10) = 0 -20 + 6/√x = 0 6/√x = 20 x = (6/20)² = 9/100
Thus, f(x) = log(-20(9/100)+ 12√(9/100)) = 0.2553
<em>The maximum value of the function is 0.2553.</em>
