Question

Which of the following is a candidate for being an extreme value for the function f(x)= -0.5x^2 2^x

Answer 1

Well, that didn't come out right...

Answer 2

it is given options of 0, 1/2 , 1 and 2

Answer 3

but my answer is so off...

Answer 4

Is this f(x)?
\[f(x)=-0.5x^2 2^x\]

Answer 5

If yes, then let's look at it closely.
\[x^2 \geq 0\ \text{and}\ 2^x>0\]
Therefore, \[x^2 2^x \geq 0 \\
\Rightarrow -0.5x^2 2^x \leq 0\]
Now, can any of 1/2, 1, and 2 be a maximum value?

Answer 6

no if it must be less or equal to 0 ! :)

Answer 7

but dont u need to find the first derivative ?

Answer 8

There's no need, really. It wasn't really asked WHAT the max value was, only which one could possibly be a max value. :D

Answer 9

oh i get it thanks so much for ur help!

Answer 10

No problem. :D