2.2.212 AP Calculus Exam problem find increasing interval

[karush]

212
Let f be the function given by $f(x)=300x-x^3$ On which of the following intervals is the function f increasing
(A) $\quad (-\infty,-10]\cup [10,\infty)$

(B) $\quad [-10,10]$

(C) $\quad [0,10]$ only

(D) $\quad [0,10\sqrt{3}]$ only

(E) $\quad [0,\infty]$
Steps

Spoiler

find first derivative to find min/max
$$y'=300-3x^2=3(100-x^2)=3(10+x)(10-x)$$
hence where $y'=0$ is at $-10,10$
an increasing interval of graph would have an positive slope so where
$$y'(0)=300$$
which is positive so the interval
$$[-10,10]\quad (B)$$

ok this was a little awkward to explain provided the answer is correct
but it was easy to get the zeros wrong due the highest power was the last term

 

[topsquark]

212
Let f be the function given by $f(x)=300x-x^3$ On which of the following intervals is the function f increasing
(A) $\quad (-\infty,-10]\cup [10,\infty)$

(B) $\quad [-10,10]$

(C) $\quad [0,10]$ only

(D) $\quad [0,10\sqrt{3}]$ only

(E) $\quad [0,\infty]$
Steps

Spoiler

find first derivative to find min/max
$$y'=300-3x^2=3(100-x^2)=3(10+x)(10-x)$$
hence where $y'=0$ is at $-10,10$
an increasing interval of graph would have an positive slope so where
$$y'(0)=300$$
which is positive so the interval
$$[-10,10]\quad (B)$$

ok this was a little awkward to explain provided the answer is correct
but it was easy to get the zeros wrong due the highest power was the last term

It looks good, but there is an error: the answer key doesn't have a correct answer!

Your analysis is good except at the endpoints. The slope of the function is 0 at the points x = -10 and x = 10. Since 0 is neither positive nor negative the endpoints cannot be part of your answer. The correct answer is (-10, 10).

-Dan

 

[skeeter]

It looks good, but there is an error: the answer key doesn't have a correct answer!

Your analysis is good except at the endpoints. The slope of the function is 0 at the points x = -10 and x = 10. Since 0 is neither positive nor negative the endpoints cannot be part of your answer. The correct answer is (-10, 10).

-Dan

according to the definition of an increasing function used by the AP folks, the closed interval is correct ...

https://teachingcalculus.com/2012/11/02/open-or-closed/