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Math Help - Need help with Derivative true/false questions

  1. #1
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    Need help with Derivative true/false questions

    Hi, can anyone tell me which of these are wrong:

    1) If f is a differentiable function at x=a, then the tangent line to the graph of f at the point (a, f(a)) is given by y-f(a) = f ' (a)(x-a) - True

    2) The derivative of a polynomial is always a polynomial - False

    3) The curve y = 2x^3 + 4x + 5 has no tangent line with slope 3 - True

    4) The function f(x) = e^x is the only function with the property that it is its own derivative - True

    5) if f ' (3) = 4 and g ' (3) = 5, then the graph of f(x) + g(x) has slope 9 at x = 3 - True

    Thanks!
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  2. #2
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    2) The derivative of a polynomial is always a polynomial - False
    Wrong, (a_n x^n + ... + a_1 x + a_0)' = na_nx^{n-1}+ ... + a_1.

    4) The function f(x) = e^x is the only function with the property that it is its own derivative - True
    What about f(x) = 0?
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  3. #3
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    Thanks. Are all the other ones correct?
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  4. #4
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    Quote Originally Posted by coldfire View Post
    Hi, can anyone tell me which of these are wrong:

    1) If f is a differentiable function at x=a, then the tangent line to the graph of f at the point (a, f(a)) is given by y-f(a) = f ' (a)(x-a) - True

    2) The derivative of a polynomial is always a polynomial - False Mr F says: The statement is true. Note that 0 is considered a polynomial ......

    3) The curve y = 2x^3 + 4x + 5 has no tangent line with slope 3 - True

    4) The function f(x) = e^x is the only function with the property that it is its own derivative - True Mr F says: The statement is false. f(x) = k e^x => f'(x) = k e^x.

    5) if f ' (3) = 4 and g ' (3) = 5, then the graph of f(x) + g(x) has slope 9 at x = 3 - True

    Thanks!
    ..
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