OpenStudy (anonymous):

Help please :) Let f(x)=54−3x−x^2. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relative maxima (minima). 1. f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima of f occur at x = 4. The relative minima of f occur at x = Notes: In the first two, your answer should either be a single interval, such as (0,1), a comma separated list of intervals, such as (-inf, 2), (3,4), or the word "none"

3 years ago
OpenStudy (anonymous):

since it is a quadratic with negative leading coefficient, it opens down therefore it is increasing from \(-\infty\) to the first coordinate of the vertex \(-\frac{b}{2a}\) and decreasing from there on

3 years ago
OpenStudy (anonymous):

@dan815

3 years ago
OpenStudy (anonymous):

ok so 1. would be from -infinity to the result from -b/2a?

3 years ago
OpenStudy (anonymous):

yes

3 years ago
OpenStudy (anonymous):

"a" would be 1 and "b" would be -3?

3 years ago
OpenStudy (anonymous):

no

3 years ago
OpenStudy (anonymous):

\[f(x)=54−3x−x^2.\] \[f(x)=-x^2-3x+54\\ f(x)=ax^2+bx+c\]

3 years ago
OpenStudy (anonymous):

ohh so -1 and -3?

3 years ago
OpenStudy (anonymous):

yes

3 years ago
OpenStudy (anonymous):

@satellite73 I typed for the first one (-inf,-.1666) and im getting it wrong

3 years ago
OpenStudy (anonymous):

@aum help!

3 years ago
OpenStudy (aum):

The function increases from x = -infinity to x = -b/2a = -(-3) / (2*-1) = 3/(-2) = -1.5 The interval is: (-infinity, -1.5)

3 years ago
OpenStudy (anonymous):

@aum so what would it be for the next 3 questions?

3 years ago
OpenStudy (aum):

It is an upside down parabola. If f(x) increases in the interval (-infinity, -1.5), it decreases in the interval (-1.5, infinity).

3 years ago
OpenStudy (anonymous):

ok

3 years ago
OpenStudy (aum):

c) x = -b/2a = -1.5. That is the vertex of the parabola. Therefore, f(x) attains its maximum at x = -1.5.

3 years ago
OpenStudy (aum):

d) the function has no relative minima.

3 years ago
OpenStudy (anonymous):

i got number 4

3 years ago
OpenStudy (aum):

That is it.

3 years ago
OpenStudy (anonymous):

could you help me in other 4 like this?

3 years ago