In scholarly or research work, how is the credibility of the writing usually proven?

To determine the credibility of an academic writing one has to take some steps, this include:
1. Checking the credentials and the affiliations of the writer from the written paper. This will allows you to know if the author has an authority by means of his qualifications to write on a particular topic.
2. Checking out the other papers that the author has written in related topic.
3. Ensuring that the work is plagiarism free by checking to see if the work was properly peer reviewed.
4. Checking the sources that the author used in his work to see if all sources are properly referenced.

You need to figure out at which x-value does the graph has a tangent line slope of -1.remember, the derivative is the slope of the tangent line. so find the derivative function and set it to equal -1 to find the x-value that will have a tangent line slope of 0.differentiate with the chain rule.    set the derivative to equal -1 and solve for x.      take log base 10 of both sides. also recall that  .    so the x-coord of the point of tangency is .the y-coordinate of this point of tangency can be calculated using the original function:     using point-slope form, the equation of the tangent line is      the x-intercept of this tangent line is when the graph is at y=0.    this rounds off to  .choice c.