The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency, a)f '(x) 0 c) f "(x) 0

Question

The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangency, a)f '(x) < 0 b) f '(x) > 0 c) f "(x) < 0 d) f "(x) > 0

sydneeod · Answer

@pooja195 please help?

sydneeod · Answer

I believe the answer is f'(x)>0

mathmale · Answer

think:  f '(x) could be interpreted as "slope of the tangent line."  Why not draw a very simiple function, choose a starting point on the graph, and then let x increase?  Will the approx. be larger than, equal to or less than the actual function value at that x?

solomonzelman · Answer

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