PLEASE HELP!a) Find the equation of the tangent

Question

 line to the graph of f(x) = (2x − 4)/(x + 1) at x = 0. (Use y for your dependent variable.)? 

 

(b) Let f(x) = 8xe^x 
For what interval is f(x) concave up? (Enter your answer using interval notation.)

 

Answer 1

(a).

The function is

To find the slope of tangent line, derivative with respect to x to the above function.

Substitute in the above equation.

To find the y-coordinate of the point, substitute in the original function.

The point-slope from of line equation is , where m = slope and is point.

Substitute  in the point-slope form of line equation.

The tangent line equation is .

Answer 2

(b).

The function is

Apply first derivative with respect to x.

Apply second derivative with respect to x.

Because when and is defined on the real line, we should be test for concavity in the interval .

Interval                    Test Value                   Sign of                                 Conclusion

                          Concave upward