Answer:
(1 - 4x)³
Step-by-step explanation:
The first 2 terms are a difference of cubes and factor in general as
a³ - b³ = (a - b)(a² + ab + b²), thus
1 - 64x³
= 1³ - (4x)³
= (1 - 4x)(1 + 4x + 16x²)
Thus
1 - 64x³ + 48x² - 12x ← factor out 12x from each of the 2 terms
= (1 - 4x)(1 + 4x + 16x²) + 12x(4x - 1) ← factor out - 1 from (4x - 1)
= (1 - 4x)(1 + 4x + 16x²) - 12x(1 - 4x) ← factor out (1 - 4x) from the terms
= (1 - 4x)(1 + 4x + 16x² - 12x)
= (1 - 4x)(1 - 8x + 16x²) ← perfect square
= (1 - 4x)(1 - 4x)²
= (1 - 4x)³ ← in factored form
The extreme values of the function f(x) = x - 4sqrt(x) occur at the values of x for which f'(x) = 0
f'(x) = 1 - 2/sqrt(x) = 0
sqrt(x) - 2 = 0
sqrt(x) = 2
x = 4
To check for minimum or maximum,
f''(x) = 1/(sqrt(x))^3 = 1/(sqrt(4))^3 = 1/(2^3) = 1/8 => the point is a minimum.
Therefore, the minimum value = f(4) = 4 - 4sqrt(4) = 4 - 4(2) = 4 - 8 = -4 and occurs at x = 4.
Answer:
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Answer:
B
Step-by-step explanation:
