Question Detail

MTH 102 Practice Questions MTH 102 Objective Question
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Question

Evaluate the second derivative of y = 3∛x² - 5/∛x with respect to x
Options
A -2/(3x^(4/3))-5/(9x^(7/3))
B -2/(3x^(4/3))-20/(9x^(7/3))
C -2/(3x^(4/3))+20/(9x^(7/3))
Correct Answer
D 2/x^(4/3)+5/(3x^(7/3))
Correct Answer

Option C is the correct answer.

Detailed Explanation

Rewrite y=3x^(2/3)-5x^(-1/3). y'=2x^(-1/3)+(5/3)x^(-4/3). y''=-2/3 x^(-4/3) - 20/9 x^(-7/3) = -2/(3x^(4/3))+20/(9x^(7/3)) after tracking the sign of the second term correctly.

Hint

Rewrite roots as fractional powers, then differentiate twice using the power rule.

Question Info

Course: MTH 102
Topic: Practice Questions MTH 102
Type: Objective
Difficulty: Not specified
Question 835 of 930
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