Explore BrainMass

Explore BrainMass

    Comparing Graphs : First and Second Derivatives

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com February 24, 2021, 2:17 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/comparing-graphs-first-and-second-derivatives-11837

    Solution Summary

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

    $2.19

    ADVERTISEMENT