- #1
Teh
- 47
- 0
will it be -26 when G'(3)MarkFL said:We are told:
\(\displaystyle G(x)=6f(x)-g(x)\)
And so we know:
\(\displaystyle G'(x)=6f'(x)-g'(x)\)
which means:
\(\displaystyle G'(3)=6f'(3)-g'(3)\)
So, what you need to do is determine from the graph the values of $f'(3)$ and $g'(3)$, and plug them into the above...:D
Teh said:will it be -26 when G'(3)
MarkFL said:What values do you get from the graph for $f'(3)$ and $g'(3)$?
MarkFL said:Around $x=3$, observe that for every increase of 1 unit in $x$, we find $f$ decreases by 3 units...thus $f'(3)=-3$, and I agree that $g'(3)=1$.
Teh said:how did you get -3 from f'(3)?
A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is essentially the slope of a tangent line at that point.
To find the derivative of a function, you can use the rules of differentiation, such as the power rule, product rule, and chain rule. These rules allow you to find the derivative of a function by manipulating the given function algebraically.
Solving a G'(3) problem allows us to find the derivative of a function at a specific point, in this case, the point with an x-value of 3. This can be useful in understanding the behavior of a function and its rate of change at that point.
No, you cannot use any method to solve a G'(3) problem. You must use a specific method, such as the rules of differentiation, to find the derivative of the given function at the specified point.
In real-life applications, finding the derivative at a specific point can help us understand the instantaneous rate of change of a quantity. This can be useful in fields such as physics, economics, and engineering, where we need to analyze the behavior of a system at a specific moment in time.