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Comparing Graphs : First and Second Derivatives

X -1.5 -1.0 -0.5 0 0.5 1.0 1.5

f(x) -1 -4 -6 -7 -6 1.0 -7

f'(x) -7 -5 -3 0 3 5 7

Let f be a function that is differentiable for all real numbers. The table above gives the values of f and its derivative f' for selected points x in the closed interval -1.5 < or equal x < or equal 1.5. The second derivative of f has the property that f''(x)>0 for -1.5<or equalx< or equal 1.5

Let graph of g be the function given by
2x^2-x-7 for x<0
g(x) = and
2x^2+x-7 for x>or equal 0

The graph of g passes through each of the points (x,f(x)) given in the table above. Is it possible that f and g are the same function? Give a detailed reason for your answers

Solution Summary

First and second derivatives are used to compare functions.
The solution is detailed and well presented.