Question

Determine the point, if any, at which the graph of the function has a tangent fine with the given siope. Function Slopey=x²+3 x quad m=-5 (x, y)=

Answer 1

To find the third derivative of y = x / e^(nx), differentiate the function three times using the quotient rule.

Step-by-step explanation:

For part a, we need to find the third derivative of the function y = x / e^(nx).

To find the third derivative, we will differentiate the function three times. Let's start by finding the first derivative:

• Using the quotient rule, the first derivative of y is y' = (1 / e^(nx)) - (nx / e^(nx)).

Then, we differentiate again to find the second derivative:

• Applying the quotient rule again, the second derivative is y'' = (-nx^2 / e^(nx)) - (2x / e^(nx)).

Finally, we differentiate one more time to find the third derivative:

• By applying the quotient rule for the third time, we can find that y''' = (2x^2 / e^(nx)) + (4nx^3 / e^(nx)) - (6nx / e^(nx)).