Use the equation m Subscript PQ Baseline equals StartFraction f left parenthesis x 1 plus h right parenthesis minus f left parenthesis x 1 right parenthesis Over h EndFraction mPQ= fx1+h−fx1 h to calculate the slope of a line tangent to the curve of the function y equals f left parenthesis x right parenthesis equals 2 x squared y=f(x)=2x2 at the point Upper P left parenthesis x 1 comma y 1 right parenthesis equals Upper P left parenthesis 3 comma 18 right parenthesis Px1,y1=P(3,18).
Use the equation m Subscript PQ Baseline equals StartFraction f left parenthesis x 1 plus h right parenthesis minus f left parenthesis x 1 right parenthesis Over h EndFraction mPQ= fx1+h−fx1 h to calc...
Let z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) , where x equals u squared plus v squared and y equals StartFraction u Over v EndFractionx=u2+v2 and y=uv. Find StartFraction partial derivative z Over partial derivative u EndFraction and StartFraction partial derivative z Over partial derivative v EndFraction∂z∂u and ∂z∂v at left parenthesis u comma v right parenthesis equals left parenthesis negative 6 comma negative 6 right parenthesis(u,v)=(−6,−6) , given that : f Subscript x Baseline left parenthesis negative 6 comma...
Given y equals f(u) and u equals g(x), find StartFraction dy Over dx EndFraction equals f prime left parenthesis g left parenthesis x right parenthesis for the following functions y equals sin, Equals 7x plus 4
Use f prime left parenthesis x right parenthesis equals ModifyingBelow lim With h right arrow 0 StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFractionf′(x)=limh→0 f(x+h)−f(x) h to find the derivative at x for the given function. s left parenthesis x right parenthesis equals 2 x plus 6s(x)=2x+6 s prime left parenthesis x right parenthesiss′(x)equals=nothing
Let f left parenthesis x comma y right parenthesis equals x squared plus y squared minus 2 y plus 1 and let R colon x squared plus y squared less or equal than space 4, shown below Let f(x,y) = x2 + y2 – 2y +1 and let R:x2 + y2 < 4, shown below. + Find the absolute extrema for f on R. f has an absolute maximum value of f has an absolute minimum value of **You only...
To construct a confidence interval for the difference between two population means mu 1 minus mu 2, use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both n 1 greater than or equals 30 and n 2 greater than or equals 30. Also, the samples must be randomly selected and independent. left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus z Subscript c Baseline StartRoot StartFraction...
Estimate the area Upper A between the graph of the function f left-parenthesis x right-parenthesis equals 1 0 s i n x and the interval left-bracket 0 comma pi right-bracket Number . Use an approximation scheme with n equals 2 comma 5 and 10 rectangles. Use the right endpoints. If your calculating utility will perform automatic summations, estimate the specified area using n equals 50 and n equals 100 rectangles.
Suppose f is differentiable on left parenthesis negative infinity comma infinity right parenthesis(−∞,∞) and assume it has a local extreme value at the point x equals 1x=1 where f left parenthesis 1 right parenthesis equals 0f(1)=0. Let g left parenthesis x right parenthesis equals xf left parenthesis x right parenthesis plus 4g(x)=xf(x)+4 and let h left parenthesis x right parenthesis equals xf left parenthesis x right parenthesis plus x plus 4h(x)=xf(x)+x+4 for all values of x. a. Evaluate g left...
Determine the domain of the function of two variables f left parenthesis x comma y right parenthesisf(x,y)equals=StartRoot y minus 3 x EndRooty−3x.
Determine ModifyingBelow lim With x right arrow c Superscript plusf(x), ModifyingBelow lim With x right arrow c Superscript minusf(x), and ModifyingBelow lim With x right arrow cf(x), if it exists. cequals3, f(x)equals left brace Start 2 By 2 Matrix 1st Row 1st Column 4 minus x 2nd Column x less than 3 2nd Row 1st Column StartFraction x Over 3 EndFraction plus 1 2nd Column x greater than 3 EndMatrix ModifyingBelow lim With x right arrow c Superscript plusf(x)equals nothing...
Suppose you have a total income of I to spend on two goods x1 and x2, with unit prices p1 and p2 respectively. Your taste can be represented by the utility function u left parenthesis x subscript 1 comma x subscript 2 right parenthesis equals x subscript 1 cubed x subscript 2 squared (a) What is your optimal choice for x1 and x2 (as functions of p1 and p2 and I) ? Use the Lagrange Method. (b) Given prices p1...