OpenStudy (anonymous):

Use the first derivative to determine where the function f(x)=4x-9x^(1/2) is increasing and decreasing

4 years ago
OpenStudy (anonymous):

can you take the derivative?

4 years ago
OpenStudy (anonymous):

4-(9/2)x^(-1/2)

4 years ago
OpenStudy (anonymous):

ok, good. so whenever that function is negative, it means the original function is decreasing and whenever its positive it means the original function is increasing.

4 years ago
OpenStudy (anonymous):

so for what values of x is your derivative positive/negative

4 years ago
OpenStudy (anonymous):

iam confused

4 years ago
OpenStudy (anonymous):

if your derivative 4-(9/2)x^(-1/2) is negative it means you function f(x)=4x-9x^(1/2) has a negative slope at that point so its decreasing. If the derivative is positive, the function f(x) has a positive slope and is increasing

4 years ago
OpenStudy (anonymous):

so what do we do next

4 years ago
OpenStudy (anonymous):

you dreivative is f'(x)=4-(9/2)x^(-1/2) or f'(x) = 4 - (9/2)* (1/x^.5) so you'll find that x^.5 is the same as sqrt(x) right? and you cant have a negative under the square root so all x values must be positive. right?

4 years ago
OpenStudy (anonymous):

yes

4 years ago
OpenStudy (anonymous):

good so if the term (9/2)*(1/x^.5)) > 4 the function f(x) will be decreasing because the derivative will be negative at that point, if its (9/2)*(1/x^.5)) < 4, it f(x) will be increasing because the derivative is positive

4 years ago
OpenStudy (anonymous):

the point where (9/2)*(1/x^.5)) = 4 is when f'(x)=0 and this is the point where if(x) switches from being a decreasing function to an increasing function

4 years ago
OpenStudy (anonymous):

hope that helps

4 years ago