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Question

The graph of f(x)=x520−x412+5 has

A
no local extreme, one point of inflection
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B
two local maximum, one local minimum, two point of inflection
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C
one local maximum, one local minimum, one point of inflection
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D
one local maximum, one local minimum, two point of inflection
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Solution

The correct option is A one local maximum, one local minimum, one point of inflection
f(x)=x520x412+5
f(x)=x44x33=x312(3x4)
For maxima or minima,
f(x)=0
x=0,43
f(x)>0 for x(,0)(43,)
f(x)<0 for x(0,43)
f′′(x)=0x3x2=0 at x=0 and 1.
f′′′(x)=03x22x=0 at x=0 and 23
x=0 cannot be a point of inflection.
Hence,
f(x) have one point of local maxima, one point of local minima, and one point of inflection.

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