Question

which of the following x-coordinates is a candidate for being an extreme value for the function f(x)=-0.5x^2(2^x)?
a) 1/2
b) 0
c) 1
d) 2
Is the answer zero?

Answer 1

There are a couple of ways to find the extreme value of a function. One way is to look at the endpoints of a function. Since this function continues infinitely in both directions, this will not work.

The second way is to look at the first derivative of a function, and set that equal to zero. So the first derivative of this function requires us to use the product rule. (I encourage you to do this part by yourself)

The first derivative is \[2^{x}*-x + -.5x^2(2^{x}*\ln2)\]
This can be factored into \[2^x(-.5x^2\ln(2) -x)\]
All you have left to do is set that equal to 0 and you'll have your answers. Or, since you have answer choices, plug them in and see which one gives you 0.

This is the Calculus method, you can also just graph it. But yes, the answer is 0.

Answer 2

thanks!