Question

Find the critical number(s) for f(x)=eˣ−2x.
a) x=2
b) x= −2
c) x=0
d) x=-1

Answer 1

The critical number for the function f(x)=e^x-2x is found by calculating the derivative and setting it equal to zero, resulting in the critical number x=ln(2), which is approximately 0.6931, not listed in the given options.

Step-by-step explanation:

The student is asking for the critical number(s) of the function f(x)=e^x−2x. To find the critical numbers, first, we need to find the derivative of the function and then set it equal to zero to solve for x. The derivative of f(x) is f'(x)=e^x−2. Setting the derivative equal to zero gives us e^x−2=0 which simplifies to e^x=2. Taking the natural logarithm of both sides gives us x=ln(2).

To find the exact value, we need to evaluate ln(2), which is approximately 0.6931. Thus, the critical number for the function is at x=ln(2), which is not one of the provided options a) x=2, b) x=−2, c) x=0, d) x=−1. Therefore, the correct answer is not listed among the options provided by the student.