04 - Relative Extrema - Kuta Software
04 - Relative Extrema - Kuta Software
04 - Relative Extrema - Kuta Software
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
-1-<br />
©H 82A0o1m3x QKmuItNaC FSmoefDtEwZa7rVeJ XLQLNCa.M 1 3AklPlA GrdiPgdhDtfs2 krLeos5eWrJvGeDdi.M S pMdaHdYea 0wBietmhH AI2nZfWiWnsiYtvey oCoaAlLcquclGutsz.q Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
<strong>Kuta</strong> <strong>Software</strong> - Infinite Calculus<br />
Name___________________________________<br />
Assignment<br />
For each problem, find all points of relative minima and maxima.<br />
1) y = x 3 − 5x 2 + 7x − 5<br />
Date________________ Period____<br />
8<br />
y<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
x<br />
−4<br />
−6<br />
−8<br />
For each problem, find all points of relative minima and maxima. You may use the provided graph to<br />
sketch the function.<br />
2) y = x 3 − 6x 2 + 9x + 1<br />
8<br />
y<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
x<br />
−4<br />
−6<br />
−8
-2-<br />
©g b2S0i1g3s QKiurt5aC XSioBfItiwXa4rKee rLCLMCb.C C dASlLld Sr li2gjhPtksV kr yeosbexr2vGe0dC.l N 4MPakdQep nwPiDtmhe jIAnQfbiAnpi6tgea RCeaMljcmu1lTuRsp.U Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
For each problem, find all points of relative minima and maxima.<br />
3) y = −x 3 − 3x 2 − 1 4) y = x 4 − 2x 2 + 3<br />
5) y = x 4 − x 2 2<br />
6) y = −<br />
x 2 − 4<br />
2<br />
3<br />
7) y = (2x − 8)<br />
8) y = − 1 5<br />
2<br />
5 (x − 4) 3 3<br />
− 2(x − 4)<br />
Critical thinking questions:<br />
9) Give an example function f (x) where f ''(0) = 0 and there is no relative minimum or maximum at x = 0.<br />
10) Give an example function f (x) where f ''(0) = 0 and there is a relative maximum at x = 0.
-1-<br />
©u u210R143j hKEuHt4as nSwo1f2tVwlagr7eE ELyLVCE.B S EAjl4lk FruiogGhUt5sf srGeisieZrhvPeZdp.9 r 6MtandseI twki0trhY 8I8nbfRiInDiotweS ACSaUlpcnuHlzuHsB.K Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
<strong>Kuta</strong> <strong>Software</strong> - Infinite Calculus<br />
Name___________________________________<br />
Assignment<br />
For each problem, find all points of relative minima and maxima.<br />
1) y = x 3 − 5x 2 + 7x − 5<br />
Date________________ Period____<br />
8<br />
y<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
x<br />
−4<br />
−6<br />
−8<br />
<strong>Relative</strong> minimum:<br />
( 7 3 , − 86<br />
27)<br />
<strong>Relative</strong> maximum: (1, −2)<br />
For each problem, find all points of relative minima and maxima. You may use the provided graph to<br />
sketch the function.<br />
2) y = x 3 − 6x 2 + 9x + 1<br />
8<br />
y<br />
6<br />
4<br />
2<br />
−8 −6 −4 −2 2 4 6 8<br />
−2<br />
x<br />
−4<br />
−6<br />
−8<br />
<strong>Relative</strong> minimum: (3, 1)<br />
<strong>Relative</strong> maximum: (1, 5)
©R u2f081i37 uKgu8t2a1 eSoo7f4tmwGa1r5ei 4LkLnCx.Y y jAhlnlg arXiUgnhutrsi HrjeFsZeFrivgepdm.v h iMJavdNep zw6iUtNho qIKnUfZi9noivtleh mCCaolDcTuQl9uns8.l Worksheet by <strong>Kuta</strong> <strong>Software</strong> LLC<br />
For each problem, find all points of relative minima and maxima.<br />
3) y = −x 3 − 3x 2 − 1<br />
<strong>Relative</strong> minimum: (−2, −5)<br />
<strong>Relative</strong> maximum: (0, −1)<br />
4) y = x 4 − 2x 2 + 3<br />
<strong>Relative</strong> minima: (−1, 2), (1, 2)<br />
<strong>Relative</strong> maximum: (0, 3)<br />
5) y = x 4 − x 2<br />
<strong>Relative</strong> minima: ( − 2<br />
<strong>Relative</strong> maximum: (0, 0)<br />
2 , − 1 4) , (<br />
2<br />
2 , − 1 4)<br />
2<br />
6) y = −<br />
x 2 − 4<br />
<strong>Relative</strong> minimum:<br />
( 0, 1 2)<br />
No relative maxima.<br />
2<br />
3<br />
7) y = (2x − 8)<br />
<strong>Relative</strong> minimum: (4, 0)<br />
No relative maxima.<br />
8) y = − 1 5<br />
2<br />
5 (x − 4) 3 3<br />
− 2(x − 4)<br />
<strong>Relative</strong> minimum: ( 0, − 12 3 2<br />
5 )<br />
<strong>Relative</strong> maximum: (4, 0)<br />
Critical thinking questions:<br />
9) Give an example function f (x) where f ''(0) = 0 and there is no relative minimum or maximum at x = 0.<br />
Many answers. Ex: f (x) = 0, x, x 3 , etc<br />
10) Give an example function f (x) where f ''(0) = 0 and there is a relative maximum at x = 0.<br />
Many answers. Ex: f (x) = −x 4 -2-<br />
Create your own worksheets like this one with Infinite Calculus. Free trial available at <strong>Kuta</strong><strong>Software</strong>.com