Ang pinakamataas na halaga ng f (x) = (3sinx-4cosx-10) (3sinx + 4cosx-10) ay?

#f (x) = (3sinx-4cosx-10) (3sinx + 4cosx-10) #

# = ((3sinx-10) -4cosx) ((3sinx-10) + 4cosx) #

# = (3sinx-10) ^ 2- (4cosx) ^ 2 #

# = 9sin ^ 2x-60sinx + 100-16cos ^ 2x #

# = 9sin ^ 2x-60sinx + 100-16 + 16sin ^ 2x #

# = 25sin ^ 2x-60sinx + 84 #

# = (5sinx) ^ 2-2 * 5sinx * 6 + 6 ^ 2-6 ^ 2 + 84 #

# = (5sinx-6) ^ 2 + 48 #

#f (x) # ay magiging maximum kapag # (5sinx-6) ^ 2 # ay maximum. Magiging posible para sa # sinx = -1 #

Kaya

# f (x) _ "max" = (5 (-1) -6) ^ 2 + 48 = 169 #

Sagot:

Pinakamataas ang 169. Minimum ay 50 (marahil, halos). Ito ay graphical illustration, para sa Dilip's answer.

Paliwanag:

Hayaan #alpha = sin ^ (- 1) (4/5) #.. Pagkatapos

#f (x) = 25 (kasalanan (x - alpha) -2) (sin (x + alpha) - 2) #

Tingnan ang graph.

graph {(y - 25 (sin (x - 0.9273) -2) (sin (x + 0.9273) -2)) (y-169) (y-50) = 0 -20 20 20 230}

graph {(y - 25 (sin (x - 0.9273) -2) (sin (x + 0.9273) -2)) (y-169) = 0 -1.75 -1.5 167 171}