Answer to Question #147640 in Algebra for liam donohue

Question

Let f(x)=8x−2ex.

Answer 1

f(x)=8x-2*e^x

Find the derivative.

f'(x)=8-2*e^x

Set the derivative equal to 0.

Solve for x.

x = ln4

After finding the point that makes the derivative f'(x)=8-2*e^x equal to 0 or undefined, the interval to check where f(x)=8x-2*e^x is increasing and where it is decreasing is ( − ∞ , ln4 ) ∪ ( ln4 , ∞ ).

( − ∞ , ln4 ) ∪ ( ln4, ∞ )

Substitute a value from the interval (-∞,4) into the derivative to determine if the function is increasing or decreasing.

Increasing on (-∞,ln4) since f ' ( x ) > 0

Substitute a value from the interval (4,∞) into the derivative to determine if the function is increasing or decreasing.

Decreasing on ( ln4, ∞ ) since f ' ( x ) < 0

List the intervals on which the function is increasing and decreasing.

Increasing on: ( − ∞ , ln4)

Decreasing on: ( ln4, ∞ )