Given The Function G X 6x 3 27x 2 180x Find The First Derivative G X G X Notice That G X 0 When X 2 1 (83.46 KiB) Viewed 42 times
Given the function `g(x)=6x^3+27x^2-180x`, find the first derivative, `g'(x)`. `g'(x)=` Notice that `g'(x)=0` when `x=2`, that is, `g'(2)=0`. Now, we want to know whether there is a local minimum or local maximum at `x=2`, so we will use the second derivative test. Find the second derivative, `g"(x)`. `g"(x)= ` Evaluate `g"(2)`. `g"(2)= Based on the sign of this number, does this mean the graph of `g(x)` is concave up or concave down at `'x=2'? [Answer either up or down watch your spelling!!] At 'x=2' the graph of a(x) is concave
Evaluate `g"(2)`. 'g"(2)= Based on the sign of this number, does this mean the graph of `g(x)` is concave up or concave down at x=2'? [Answer either up or down watch your spelling!!] At `x=2 the graph of `g(x) is concave Based on the concavity of `g(x)` at `x=2`, does this mean that there is a local minimum or local maximum at `x=2¹? [Answer either minimum or maximum -- watch your spelling!!] At x=2 there is a local
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