Question

.8 Let f(x) have second order derivate at c such that f'(c)=0 and f"(c)>0, then c is a point of *​

Answer 1

Given :   f(x) have second order derivate at c such that f'(c)=0 and f"(c)>0

To Find : c is a point of  

inflexion

local maxima

local minima

None of these

Solution:

f(x)  is any function

f'(c) = 0

f''(c)  > 0

hence c is a point of Local Minima

f(x)  is any function

f'(c) = 0

f''(c)  <  0

hence c is a point of Local Maxima

Local Minima   is correct answer

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Answer 2

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GIVEN

Let f(x) have second order derivate at c such that f'(c)=0 and f"(c)>0

TO DETERMINE

c is a point of which type

EVALUATION

THEOREM :

If c is an interior point of the domain of a function f and f'(c) = 0 , then the function has a maxima or a minima at c according as f''(c) is negetive or positive

As a consequence of the above Theorem, if f' vanishes at c, then c is a point of maxima if f''(c) < 0 and a minima if f''(c) > 0

RESULT

Hence for the given function f(x) and with the given condition :

c is a point of Local minima

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