Question

F'(0) = 3, g(x)=f(-x), g'(0) =?​

Answer 1

Ответ:

Пошаговое объяснение:

f`(0)=3x²-6x

g`(0)=1/√x

(3x²-6x)/√x=0,x>0

3x(x-2)/√x=0

3√x*(x-2)=0

√x=0

x=0

x=2

Answer 2

If you know that $F'(0) = 3$ and $g(x) = f(-x)$, you can find $g'(0)$ using the chain rule for differentiation.

The chain rule states that if you have a composite function $h(x) = f(g(x))$, then its derivative $h'(x)$ is given by:

$h'(x) = f'(g(x)) \cdot g'(x)$

In this case, you want to find $g'(0)$, so $x = 0$. Therefore, the equation becomes:

$g'(0) = f'(g(0)) \cdot g'(0)$

Since $g(x) = f(-x)$, $g(0) = f(0)$. So, the equation becomes:

$g'(0) = f'(f(0)) \cdot g'(0)$

Now, you're given that $F'(0) = 3$, which is the derivative of $f(x)$ at $x = 0$. So, $f'(0) = 3$.

Therefore, the equation further simplifies to:

$g'(0) = 3 \cdot g'(0)$

Now, you can solve for $g'(0)$ by dividing both sides of the equation by 3:

$g'(0) = \frac{3 \cdot g'(0)}{3}$

This simplifies to:

$g'(0) = g'(0)$

So, $g'(0)$ is equal to itself. In this form, you can't determine its exact value without additional information about the function $g(x)$.