Question to test your Intro to Extrema knowledge

Question

Analyze the given graph of the function $f (x)$ on the interval $open bracket negative 5 comma 2 close bracket$ to find the intervals where the function is increasing or decreasing, and identify its local and absolute extreme values.

Accepted Answer

Increasing: (−3,−2)∪(0,2)\left(-3,-2ight)\cup\left(0,2ight)Decreasing: (−5,−3)∪(−2,0)\left(-5,-3ight)\cup\left(-2,0ight)Local minimum: f(−3)=1 and f(0)=−1f\left(-3ight)=1	ext{ and }f\left(0ight)=-1Local maximum: f(−2)=2f\left(-2ight)=2Absolute minimum: f(0)=−1f\left(0ight)=-1Absolute maximum: f(−5)=3f\left(-5ight)=3

Answer

Increasing: (−5,−3)∪(−2,0)\left(-5,-3ight)\cup\left(-2,0ight)Decreasing: (−3,−2)∪(0,2)\left(-3,-2ight)\cup\left(0,2ight)Local minimum: f(−3)=1 and f(0)=−1f\left(-3ight)=1	ext{ and }f\left(0ight)=-1Local maximum: f(−2)=2f\left(-2ight)=2Absolute minimum: f(0)=−1f\left(0ight)=-1Absolute maximum: f(−5)=3f\left(-5ight)=3

Answer

Increasing: (−3,−2)∪(0,2)\left(-3,-2ight)\cup\left(0,2ight)Decreasing: (−5,−3)∪(−2,0)\left(-5,-3ight)\cup\left(-2,0ight)Local minimum: f(−2)=2f\left(-2ight)=2 Local maximum: f(−3)=1 and f(0)=−1f\left(-3ight)=1	ext{ and }f\left(0ight)=-1Absolute minimum: f(0)=−1f\left(0ight)=-1Absolute maximum: f(−5)=3f\left(-5ight)=3

Answer

Increasing: (−3,−2)∪(0,2)\left(-3,-2ight)\cup\left(0,2ight)Decreasing: (−5,−3)∪(−2,0)\left(-5,-3ight)\cup\left(-2,0ight)Local minimum: f(−3)=1 and f(0)=−1f\left(-3ight)=1	ext{ and }f\left(0ight)=-1Local maximum: f(−2)=2f\left(-2ight)=2Absolute minimum: f(−5)=3f\left(-5ight)=3Absolute maximum: f(0)=−1f\left(0ight)=-1

Intro to Extrema: Videos & Practice Problems

Analyze the given graph of the function f(x)f\(\left\)(x\(\right\)) on the interval [−5,2]\(\left\[\lbrack\)-5,2\(\right\]\rbrack\) to find the intervals where the function is increasing or decreasing, and identify its local and absolute extreme values.

Analyze the given graph of the function $f (x)$ on the interval $open bracket negative 5 comma 2 close bracket$ to find the intervals where the function is increasing or decreasing, and identify its local and absolute extreme values.