Question

F(x)=(7+x)e −4xWhat is the value of x at which the function has a possible relative maximum or minimum point?

x = ___________
Is the point a relative maximum or minimum?
A minimum
B maximum

Answer 1

The function f(x) = (7+x)e^-4x has a possible relative extremum at x = -29/4. To determine if it's a maximum or minimum, the second derivative or a first derivative test must be analyzed.

Step-by-step explanation:

To determine where the function f(x) = (7+x)e-4x has a possible relative maximum or minimum, we need to find the first derivative of the function and set it equal to zero to solve for x.

First, we apply the product rule of differentiation to the function:

f'(x) = d/dx [(7+x)e-4x] = e-4x d/dx [7+x] + (7+x) d/dx [e-4x] = e-4x - 4(7+x)e-4x.

Setting the first derivative equal to zero to find critical points:

e-4x - 4(7+x)e-4x = 0

Simplifying, we get:

1 - 4(7+x) = 0

Solving for x:

x = -1 - 7/4 = -29/4

The value of x at which the function has a possible relative maximum or minimum point is -29/4.

To determine whether this point is a relative maximum or minimum, we must evaluate the second derivative or use the first derivative test. Since this information is not provided in the question, we can only supply the critical value and would need additional analysis to determine the nature of the extremum.