Question

Find the extrema (x and y values, type) and zeros of .01(x + 1.5)^3 (x − 2)^2 (x + 3)^4

Answer 1

Stepg to fnd exhrema (1) Calaulate first derivative dd eguate d Critl bonts whch wil be values, to fnd the (1) Colautote 2nd dervative Cmd but each rik'tal bonts check the Sign of d d dy at hat crMcal bont exists etrema minima ess at that C al bojns Now 0 04 0-02 (-2)1' (n+ the producd rule of devatve d(uv Apb uw dv - uy duo vw du 0 04 -D-02 (mane) (x+3 -2) (+1 5) (u3}o0+ (m-2) (m41s) +0 03 (m 4) (+1)(4) (-(n+(4) 0 (n> osm-2)+oi03(w^en-e) +0-02(n24.5 +45) 0 02 O1 0.2 n2 -1S -3 1.06986 -2.18097 CHtal bomts

fon equato O, do2 o0 46 -2)1s)(3+ 0.06 (-2)^ ( 1s) (n+) +012 (x- 5) +0.02 (* +1$)* (x + )* at d 2 0.02 2+)3 (2+3)>0 o exist at nE 2 manima at -S ol2 aut -1 211SS <o dn2 at -2.18 037 0 31165I Jo nima e1' Hence 1 (1)3-2)(u*j)t hos extrema. at o.01 069 86 at whch 40-28496 0-01 (15)-2+)+ 2eTog wil be -1S, 2 ,-3 ot