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Calculus
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Jun 15th, 2015

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Jun 15th, 2015

given f(x) =  -x^2  + 4x + 5     x<4

                 =   2x - 3    x>=4


so now to check for continuous we    have    to find f(x+) and f( x-)

f( x+) means the value of f(x) where x>=4

f( x -) means the value of f(x) where x <4


f( 4 + )  we have to find so just plug  x=4  in f(x) where x>=4

so f( 4+) = -(4)^2 + 4(4) +5

               = -16  + 16 +5

f(4+) = 5

now in similer way i will find f (x -)   that is f(4 -)

f(4 -) = 2(4)  -3

         = 8 - 3

         = 5

so the value of f( 4+ ) and f( 4-) values are 5

both are same so the given function is continuous

Jun 15th, 2015

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