Find $g'(3)$ if $g(x)$

Question

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

Answer 1

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

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

Answer 2

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...

Answer 3

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.

Answer 4

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