Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.


Mathematics

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Find all critical numbers for the function. State whether it leads to a local maximum, a local minimum, or neither.f(x) = 

A. No critical numbers; no local extrema B. Local maximum at -5; local minimum at 1 C. Local minimum at 1 D. Local maximum at -5

Mathematics

Find the foci of the ellipse whose equation is given. +  = 1

A. foci at (-3, -1 - ) and (-3, -1 + )
B. foci at (3, -1 - ) and (3, -1 + )
C. foci at (-2, -1 - ) and (-2, -1 + )
D. foci at (-1, -3 - ) and (-1, -3 + )

Mathematics

Solve the problem.Sales (in thousands) of a certain product are declining at a rate proportional to the amount of sales, with a decay constant of 8% per year. By writing and solving a differential equation, determine how much time will pass before sales become 60% of their original value. 

A. 5.7 years B. 7.3 years C. 6.8 years D. 6.4 years

Mathematics

Given that 1 yard = 3 feet, find the number of cubic feet in 1 cubic yard.

A. 27
B. 9
C. 3
D. None of These

Mathematics