Given to the right is the graph of the function fx x3 3x2

Given to the right is the graph of the function f(x) = x3 + 3x2 - 3x + 3. Graphically estimate the value(s) of x at which f has a horizontal tangent line. Then, use derivatives to find more accurate estimates. Find all values of x at which the tangent line to f is parallel to the line y = 6x + 6.

Solution

a)from graph its nearly2.5 and 0.5 y\'=0 3x^2 +6x-3=0 ==>x=-2.414,0.414 b)3x^2 +6x-3=6 ==>x=-3,1
 Given to the right is the graph of the function f(x) = x3 + 3x2 - 3x + 3. Graphically estimate the value(s) of x at which f has a horizontal tangent line. Then

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