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rjkz [21]
3 years ago
15

State the number of possible real zeros and turning points of f(x) = x7 – 6x6 + 8x5. Then determine all of the real zeros by fac

toring.
=
Mathematics
1 answer:
Rudiy273 years ago
3 0

Answer:

steps below

Step-by-step explanation:

f(x) = x⁷ – 6x⁶ + 8x⁵

f'(x) = 7x⁶ - 36x⁵ + 40x⁴

      = x⁴ (7x² - 36x + 40)   ... (1)

Critical point (x,y): x = 0  ,  x = (36 ± √(-36)²-4*7*40) / (2*7) = (18±2√11) / 7

x = 0   or   x = 3.5    or    x = 1.6

plug into (1): y = 0   ,  y = -394.3  ,    y = 10.1

extreme : <u>maximum (1.6 , 10.1)</u>       <u>minimum (3.5 , -394.3)</u>  ... turning points

x⁷ – 6x⁶ + 8x⁵ = x⁵ (x² - 6x + 8) = x⁵ (x-2) (x-4) =0

<u>real zeros: x = 0,   x=2,    x=4</u>

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