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
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
$g'(x)=6*x-5*f'(x)$
$g'(3)=6*3-5*f'(3)$=$18-25=-7$ i hope it would help you
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...
Since it's a homework question here are some tips.
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 $g'(3) = 6\cdot 3 - 5 f'(3) = 18 - 5 \cdot 5 = 18 - 25 = -7$.