Question
Let f be a function such that f(x+y)=f(x)+f(y) for all x and y and f(x)=(2x2+3x)g(x) for all x where g(x) is continuous and g(0)=9 then f'(0) is equals to
Answer: Option C
:
C
f′(x)=limh→0f(x+h)−f(x)h
=limh→0f(x)+f(h)−f(x)h
=limh→0(2h2+3h)g(h)h
=limh→0(2h+3)g(h)
=3g(0)
=27
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:
C
f′(x)=limh→0f(x+h)−f(x)h
=limh→0f(x)+f(h)−f(x)h
=limh→0(2h2+3h)g(h)h
=limh→0(2h+3)g(h)
=3g(0)
=27
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