Calculus Answers

Find nature of root of polynomial 2x^5+x^3+5x+1

Find
dz/dt
for z = x^2 y + 4y^2 where x = cost and y = sin t using the chain rule

Express the function g:R_R. Defined by th g(x) as the composition of the three

What is the shortest distance from the surface xy+12x+z^2=144 to the origin?

distance = ?

Use Lagrange multipliers to find the point (a,b) on the graph of y=e^8x, where the value ab is as small as possible.

P=?

Find the absolute extrema of f(x, y) = x^(2).y − 2.x + y on the
closed triangle T with vertices (1, 0),(5, 0) and (1, 4).

Find the maximum and minimum values of the function f(x,y)=2x^2+3y^2−4x−5 on the domain x2+y2≤225.

What is the maximum value of f(x,y)?


List the point(s) where the function attains its maximum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7).

What is the minimum value of f(x,y) ?


List points where the function attains its minimum as an ordered pair, such as (-6,3), or a list of ordered pairs if there is more than one point, such as (1,3), (-4,7).

Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x−2y subject to the constraint x^2+y^2=5, if such values exist.

maximum = ?

minimum = ?

Find the points on the ellipse x^2 + 16y^2 = 16 that are furthest
away from the point (0, −1) using the method of Lagrange Multipliers.