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if $f(3)=-2$ and $f'(3)=5$, find $g'(3)$ if,
$g(x)=3x^2-5f(x)$

the answer is -7, I find that very hard to understand the question. thanks

  • 4
    $g(x) = 3x^2 - 5f(x)$ if you derive this expression wrt $x$, you get $g'(x) = 6x - 5f'(x)$ (assuming everything is nice and differentiable). Plugging the numbers yields the answer.2012-04-22

4 Answers 4

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$g'(x)=6*x-5*f'(x)$

$g'(3)=6*3-5*f'(3)$=$18-25=-7$ i hope it would help you

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    sorry 4 another question,i did this another question $\frac{3x+1}{f(x)}$ it doesn't work.2012-04-22
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Hint:

  • $(\alpha+\beta)\ '=\alpha\ '+\beta\ '$

  • $f$ is differentiable at $x=3$ as $f\ '(3)$ exists.

  • $f(3)$ is not a relevant piece of information here...

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    @SbSangpi The key is quotient rule for taking derivatives--One hint is that you _need_ the information about $f(3)$...Please try this out on your own. If you still have difficulties--ping me back here. Regards,2012-04-23
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Since it's a homework question here are some tips.

  1. Are $f,g$ differentiable functions everywhere??If not, how can you find the derivative of $g$ at a specific point (in our case 3).
  2. Find everything needed for calculating $g'(3)$ from the equation given.
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The solution to the problem comes from the fact that differentiation is a linear operator. This means that $(cf(x) + dg(x))' = cf'(x) + dg'(x)$ where $c$ and $d$ are constants. Assuming we know this and the differentiation rule for powers ($(x^n)' = n x^{n-1}$) we can continue by differentiating the equation $g(x) = 3x^2 - 5f(x)$ to get $g'(x) = 6x - 5f'(x).$

Therefore $g'(3) = 6\cdot 3 - 5 f'(3) = 18 - 5 \cdot 5 = 18 - 25 = -7$.