derivative calculus

Please help.

f(t)=(4+√t)(4t^2-5)

This is what I have so far...

(4+√t)(8t)+(4t^2-5) (1/2t^-1/2)

Am struggling to get this in factored form. Am working on a multiple choice take home test and nothing I am getting matches.

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  1. the derivative you got is correct.
    by distributing, we can further simplify this into:
    32t + 8t^(3/2) + 2t^(3/2) - (5/2)t^(-1/2)
    10t^(3/2) + 32t - (5/2)t^(-1/2)

    hope this helps~ :)

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  2. sofar ok
    why don't we expand this ... and simplify to get

    32t + 10t^(3/2) - (5/2)t^(-1/2)
    = 32t + 10t√t - 5/(2√t)

    Since I don't know what your choices are, I don't know in which direction to go from here.

    Here is a good trick to see if your answer is the same as theirs.
    Pick any point on the original
    e.g. let t = 1
    f(1) = 5(4-5) = -5

    so (1,-5)
    so sub in t = 1 into our derivative answer to get
    32(1) + 10(1)(1) - 5/(2(1)) = 39.5
    Any of the choices not giving you 39.5 would be incorrect.

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  3. Here are my options

    a) 10t^2+32t√t - 5 / √t

    b) 20t^2-64t√t - 5 / 2√t

    c) 20t^2+ 32t√t - 5 / 2√t

    d) 20t^2+64t√t - 5 / 2√t

    e) 10t^2-32t√t - 5 / √t

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  4. added

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  5. If c) is written as
    (20t^2 + 32t√t - 5)/(2√t) it would be same as my answer.
    The formed a common denominator

    the way you typed it, only the -5 would be divided by 2√t

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  6. Thanks. I see my mistake now.

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