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Home Question Bank Math Calculus Archive 2024 November 24

Calculus Questions from Nov 24,2024

Browse the Calculus Q&A Archive for Nov 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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A T-shirt manufacturer is planning to expand its workforce. It estimates that the number of \( T \)-shirts produced by hiring \( x \) new workers is given by \( T(x)=-0.75 x^{4}+27 x^{3} \), \( 0 \leq x \leq 27 \). When is the rate of change of \( T \)-shirt production increasing and when is it decreasing? What is the point of diminishing returns and the maximum rate of change for \( T \)-shirt production? Graph \( T \) and \( T^{\prime} \) on the same coordinate system. The rate of change of T-shirt production is increasing on (Type your answer in interval notation.) Calcular el área limitada por la gráfica de las funciones \( y=3 x^{2} \) y \( y=-x^{2}+4 x \) A dairy is planning to introduce and promote a new line of organic ice cream. After test marketing the new line in a large city, the marketing research department found that the demand in that city is given approximately by the following equation, where \( x \) thousand quarts were sold per week at a price of \( \$ p \) each, and whose revenue function is given as \( R(x)=x p \). \( p=9 e^{-x} \quad 0<x<7 \) (A) Find the local extrema for the revenue function. (B) On which intervals is the graph of the revenue function concave upward? Concave downward? Find all local maximum and minimum points of \( f(x)=12 x-x^{3} \) on the interval \( [-3,1] \). local min at \( x=-2 \), local max at \( x=2 \) local min at \( x=-2 \), no local max. local min at \( x=2 \), local max at \( x=-2 \) local max at \( x=2 \), no local min. none of the above. Find the \( x \) and \( y \) coordinates of all inflection points. \( f(x)=x^{3}+21 x^{2} \) True or False: A global maximum of a function \( f(x) \) is a number \( M \) such that \( f(x) \leq M \) for all \( x \) in the domain of \( f(x) \) True False True or False; \( A \) local minimum of a function \( f(x) \) is a number \( m \) such that \( f(x) \geq m \) for all \( x \) the domain of \( f(x) \). True False True or False: A critical number of a function \( f(x) \) is a number \( c \) such that \( f(c)=0 \) True False Find \( f^{\prime \prime}(x) \) \[ f(x)=\left(x^{2}+6\right)^{4} \] Find the indicated derivative for the function. \( f^{\prime \prime}(x) \) for \( f(x)=7 x^{7}-2 x^{5}+2 x-2 \)
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