Given the function g(x) = 6x° + 72r² + 270z, find the first derivative, g' (1). gʻ(x) = Notice that g'(x) = 0 when z - 3, that is, g'( – 3) = 0. Now, we want to know whether there is a local minimum or local maximum at z = - 3, so we will use the second derivative test. Find the second derivative, g"(r). g*(x) = Evaluate g"( – 3). s'( – 3) =| Based on the sign of this number, does this mean the graph of g(x) is concave up or concave down at I = - 3? [Answer either up or down -- watch your spelling!!] At z - 3 the graph of g(x) is concave - 3, does this mean that there is a local minimum or local Based on the concavity of g(x) at z maximum at z = - 3? [Answer either minimum or maximum -- watch your spelling!!] At * = – 3 there is a local

Q: y" y' = Note: You can earn partial credit on this problem. Find the inflection points of f(x) = 6x4…

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Q: Find the absolute maximum and minimum, if either exists, for f(x) = x - 8x + 9. Find the first…

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

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Q: Find the first and second derivative if w = 3z-2-(1/z)

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Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: For the function f(x), we know that f(8) = 10 and f’ (8) = -1. Use the derivative to provide an…

A: By linear approximation :fx=f8+x-8f'8=> fx=10+(x-8)(-1)=> f(x)=10-x+8=> f(x)=18-x