Find Derivative: Solve G'(3) Problem

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In summary, we are trying to find the value of G'(3) by plugging in the values of f'(3) and g'(3) into the equation G'(x)=6f'(x)-g'(x). From the given information, we know that f'(3) = -3 and g'(3) = 1. By plugging these values into the equation, we can determine that G'(3) = -26.
  • #1
Teh
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View attachment 6132

Does it want me to plug in G'(3) into the equation?
 

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  • #2
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
 
  • #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
will it be -26 when G'(3)
 
  • #4
Teh said:
will it be -26 when G'(3)

What values do you get from the graph for $f'(3)$ and $g'(3)$?
 
  • #5
MarkFL said:
What values do you get from the graph for $f'(3)$ and $g'(3)$?

you get f'(3) = 6 and g'(3) = 1
 
  • #6
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 $g'(3)=1$.
 
  • #7
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 $g'(3)=1$.

how did you get -3 from f'(3)?
 
  • #8
Teh said:
how did you get -3 from f'(3)?

Rise over run...rise is -3 when run is 1...:D
 

FAQ: Find Derivative: Solve G'(3) Problem

What is a derivative?

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.

How do you find the derivative of a function?

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.

What is the purpose of solving a G'(3) problem?

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.

Can you use any method to solve a G'(3) problem?

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.

How can finding a derivative at a point be useful in real-life applications?

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.

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