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    Functions, derivatives, and critical numbers

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    Please show me how to reach correct solutions. Please see the attached file.
    Thanks in advance,
    Find f(x), given that...
    Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.
    Find the critical numbers...

    © BrainMass Inc. brainmass.com December 15, 2022, 6:47 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/functions-derivatives-critical-numbers-172686

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    Please see the attached file for answers. Thanks.

    1. Find f(x), given that

    for all x and

    Answer:

    First integrate the expression using the power rule and trig identities. (hint: the derivative of the sin function is the cosine function)

    f(x) = 10x2 + 3 sin(x)+ C

    Now plug in f(0) = 2 and solve for C

    f(0) = 10(0)2 + 3 sin(0)+ C = 2
    0 + 0 + C = 2
    C = 2

    So the total equation now becomes

    f(x) = 10x2 + 3 sin(x)+ 2

    2. Given that f is a differentiable function and the graph of its derivative is shown below, find the interval(s) in which f is decreasing.

    Answer:

    We can look at the graph and see it is ...

    Solution Summary

    This shows how to find a function from the derivative and the graph of the derivative, as well as finding critical numbers and extrema.

    $2.49

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