Need help with Derivative true/false questions

• October 6th 2008, 06:50 PM
coldfire
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!
• October 6th 2008, 07:38 PM
ThePerfectHacker
Quote:

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

Quote:

4) The function f(x) = e^x is the only function with the property that it is its own derivative - True
What about $f(x) = 0$?
• October 6th 2008, 07:42 PM
coldfire
Thanks. Are all the other ones correct?
• October 6th 2008, 08:49 PM
mr fantastic
Quote:

Originally Posted by coldfire
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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