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100 POINTS.

PLEASE PROVIDE STEP BY STEP ANSWER

THANK YOU.

100 POINTS. PLEASE PROVIDE STEP BY STEP ANSWER THANK YOU.-example-1
User Splungebob
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2 Answers

5 votes

Answer:

W'(0) = -24

Explanation:

User Psudo
by
7.8k points
5 votes

Explanation:

W(x) = (10x⁴ − 8) (30x + 25)^0.5

A) Take log of both sides.

ln(W) = ln[(10x⁴ − 8) (30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + ln[(30x + 25)^0.5]

ln(W) = ln(10x⁴ − 8) + 0.5 ln(30x + 25)

Take derivative.

W' / W = 40x³ / (10x⁴ − 8) + 0.5 (30) / (30x + 25)

W' / W = 20x³ / (5x⁴ − 4) + 3 / (6x + 5)

W' = W [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

W'(x) = (10x⁴ − 8) (30x + 25)^0.5 [20x³ / (5x⁴ − 4) + 3 / (6x + 5)]

B) Evaluate at x = 0.

W'(0) = (0 − 8) (0 + 25)^0.5 [0 / (0 − 4) + 3 / (0 + 5)]

W'(0) = (-8) (5) (0 + 3/5)

W'(0) = -24

User Lilawood
by
8.0k points

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