Sketch the graph of f with emphasis on concavity. Label asymptotes with their equations and important points with coordinates.
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- multivariate calculus Partially differentiate the follwoing with respect to x1 and x2Find the area in square units of the region under the graph of the function f on the interval[-10,5] using the fundamental theorem of calculus then verify the result using geometry f(x) = 5Divergence Thereom help please?
- Anti-derivatives of VVFsApplying the Second Derivative Test Find the critical points of f (x, y) = (x2 + y2)e-x and analyze them using the Second Derivative Test.Find the area (in square units) of the region under the graph of the function f on the interval [−6, 11], using the Fundamental Theorem of Calculus. Then verify your result using geometry. f(x)=8 ______ square units
- A right triangle has one vertex on the graph of y = x3, x > 0, at (x, y) another at the origin, and the third on the positive y-axis at (0, y). Express the area A of the triangle as a function of x.Using the First Derivative Test proved in the videos, prove the following version of the First Derivative Test: If f′ is continuous on the interval [a,b] and if f has exactly one critical point c then f has a maximum at c if f′(a′)>0 and f′(b′)<0 for some a′ and b′ such that a<a′<c<b′<b.Deduction of the second derivative criterion for optimization of functions <br> of two variables using and as related to Taylor