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- Find the value a>0 such that the tangent line to the graph of f(x) = x^2(e^-7x) at x = a passes through the origin.Find the length of the graph of the function y = ln (1 - x2), 0 ≤ x ≤ 1/2.Find the equation of the line that is tangent to the graph of the function f(x) = ln(8x + 6) at the point (0, ln 6).
- Find the inflection points of the function f(x) = ln(x^2 + 1)Find the absolute maximum and absolute minimum of the function f ( x ) = x 2 e -x on the closed interval [ 1 , 4 ].find the average rate of change of g(x)=x3-2x+1 from 1 to 3. average rate of change for function g(x) over the interval [1,3]
- find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln xDisprove the statement ln(xy) = (ln x)(ln y) by, a) Letting y equal a positive constant of your choice, and b) Using a graphing utility to graph the function on each side of the equal sign. The two functions should have different graphs, showing that the equation is not true in general.The location of the point of inflection in the graph of the function y = x ln x is at