Finding ?f? from ?f??? Sketch the graph of ?f?(?x?) = ?x? (the derivative of ?f?). Then, sketch a possible graph of ?f?. Is there more than one possible graph?
SOLUTION STEP 1 The graph of(x) = x is Since this is a graph of derivative,we can understand that it is the slope of the original graph. Here,we can observe that the slope is positive for values x > 0 and is negative for values x < 0. STEP 2 Therefore the possible graph of the function can be STEP 3 Given f (x) = x On integrating ,we get f(x) = 2 +c,where c is any real number. Therefore there is infinitely many possibilities of graph of f(x)