Math Problem Statement
Determine the intervals on which the following function is concave up or concave down. Identify any inflection points. f left parenthesis x right parenthesisequalsStartRoot 4 x EndRoot ln left parenthesis x right parenthesis Question content area bottom Part 1 Determine the intervals on which the following functions are concave up or concave down. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice. A. The function is concave up on enter your response here and concave down on enter your response here. (Simplify your answers. Type your answers in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) B. The function is concave down on enter your response here and the function is never concave up. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) C. The function is concave up on enter your response here and the function is never concave down. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed. Use integers or fractions for any numbers in the expression.) D. The function is never concave up nor concave down. Part 2 Locate any inflection points of f. Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. An inflection point occurs at xequals enter your response here. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There are no inflection points for f.
Solution
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Math Problem Analysis
Mathematical Concepts
Differentiation
Concavity
Inflection Points
Product Rule
Quotient Rule
Logarithmic Functions
Square Root Functions
Formulas
First derivative: f'(x) = (ln(x) + 1)/√x
Second derivative: f''(x) = (1/x)√x - (ln(x) + 1)/(2√x)
Theorems
Product Rule of Differentiation
Quotient Rule of Differentiation
Suitable Grade Level
Grades 11-12
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