Use the given graphs of f and g to find each derivative.

Question

c. d/dx ((f(x) / g(x)) |x=3

Accepted Answer

Evaluate the following derivatives using the graph given below. Where we have the derivative of FXX divided by G of X at X equals -1. We're also given a graph of a function here to help us solve our derivative. Now, to solve this, we will be making use of The quotient rule. Or derivatives. This rule is given by F X G of X minus F of X G X All divided by GMX, squick. Since we are at X equals -1, We will say F of -1. G of -1 minus F of -1. G of -1. All divided by a G of -1. Square Now, let's find each of these different values. You first have F of -1. Now, to solve this, we need to find the derivative of The line for F of X. Which we will use the slope of the graph. So we see Native one is on the left side of this function, so we need to find the slope of this left section. Let's find 2 points. We have one At 10 and 1 also. At 04. So, the value F-1 is the slope between these two points. Which is the change in Y divided by the change in X. Or 4 minus 0. Divided by 0 minus -1. This gives us 4 divided by 1, which is just 4. So now we have F of -1. Let's find G of -1. Well, if we look at our graph, G of neither one. Corresponds with a value. of -2. We will say negative too. F of neither one. As mentioned before, and our point is 0. And finally G-1 will be the slope. Of the G of X line. Where we can use 2 points, -1, -2. And 2-1. We get -1 minus -2. Divided by 2 minus -1. This gives us 1 divided by 3 or 1/3. We now have all of our values for our derivative function. We have F of -1. Which is sport. Multiplied by G of -1. 2 Minus F of 91, which is 0, multiplied by 134 G of -1. This is all divided by -2 squared. We then have -8 minus 0. Divided by positive 4. Which gives us -2. This means the slope, I'm sorry, not a slope, or derivative actually, of this function is negative 2. OK, I hope to help you solve the problem. Thank you for watching. Goodbye.

Use the given graphs of f and g to find each derivative. <IMAGE>
c. d/dx ((f(x) / g(x)) |x=3

Key Concepts

Derivative

Quotient Rule

Evaluating Derivatives at a Point

Watch next