Relative extrema of the function f(x) = 15 + 16x - x^2

[jself]

I do not understand this section at all. I don't even understand what they are doing in the example problems. Please, I need someone to go through this step by step explaining everything they are doing. Thank you.

The instructions say: Find all relative maximum and minimum points of each function.

The function is f(x) = 15 + 16x - x^2

 

[stapel]

Since we cannot teach courses here, it would be helpful if you clarified where you are stuck. I would think that the book and your instructor were fairly explicit in saying that the first step in finding max/min points is to take the derivative. How far have you gotten with that? Then you're supposed to set the derivative equal to zero, and solve. How far have you gotten with that? And so forth.

Please be specific. Thank you.

Eliz.

 

[jself]

I know that you are not here to teach me. However, I am taking courses online which can make it fairly difficult to interact with my instructor.

I started finding the derivative , but I am not sure if I am doing it correctly.

16-2x=0

x=-16 x=0

The book was saying to find an x value on each side of the critical number.

f'(-1)= 15+16x-x^2= 15+16(-1)-(-1)^2= -1+1=0

f'(0)= 15 +16(0) - 0^2= 15

f'(1)= 15+ 16(1)-1^2= 15+16 -1= 30



f'(-17)= 15+16(-17)-(-17^2)= 32

f'(-16)= 15 +16(-16)-(-16^2)= 15

f'(-15)= 15 +16(-15)-(-15^2)= 0

I have absolutely no idea what to do with the problem form here. I also am not even sure if this is how you work it thus far.

 

[skeeter]

I know that you are not here to teach me. However, I am taking courses online which can make it fairly difficult to interact with my instructor.

I started finding the derivative , but I am not sure if I am doing it correctly.

16-2x=0

if f'(x) = 16 - 2x = 0, x = 8 ... not -16 or 0.

for x < 8, f'(x) > 0 ... f(x) is increasing
for x > 8, f'(x) < 0 ... f(x) is decreasing

so ... since the sign of f'(x) changes from positive to negative at x = 8, f(8) is a maximum.

 

[stapel]

16-2x=0

x=-16 x=0

It looks like you're having trouble with algebra, because 16 - 2x = 2(8 - x) = 0 has only one solution: x = 8.

Eliz.

 

[jself]

I forgot to factor the 2 out of the equation. So when I subtracted 16 from both sides I was left with x=-16. And with the -2x I was subtracting -2 from 0 which left me with x=0. Thank you for your help.