Question

function y = f(x) and its derivative y= f'(x), but whoever made these graphs forget to label which one is which. First, describe the graphs of these functions. What are some key features of the graph? Imagine your are trying to describe the graph to someone who cannot see it. Which graph is the function and which one is the derivative? Explain in 100 words how you arrived at your answer.

Answer 1

Q: I Sol. In • The mathematics f is The graph of a of all function set of in so derged pairs (27) where as So when we see The first derivative of f ise. f is same thing slope of fi graph of The graph of ist derivative is going up a (or down) goining up for down) . we Can Think That is slope a Deseription of graphs of f &f. → An increasing intervail on to on interval The function corresponds graph of it's derivaline for some single point inflection point). That is Positive for Zero if The function has horizontal In other words, с part of The Corresponds to graph That's function's increasing interval derivative ne-anis for That Touches Some single point). above x-anis for

on function interval for a horizontal ₃ A decreasing internal Corresponds to negative а graph of derivative (or Tero single Point if The function inflection Point). In other words The functions decreasing interval corresponds to a part of derivative graph below x-anis (or Touches x-anis at single point incase of horizontal inflection point), that's function corresponds an interval a → A local maxima of graph of to Zero (an x-intercept) the graph of it's derivative x-anis, going down. That Crosses لحم ما A و on The function to an minimum graph of Correspond Zero (an no intercept) interval of graph of it's derivatine The a-anis going up. That crosses f(x)= x² ful = 2X