Question
Check whether the function given by:
has local maxima and local minima.
Answer :
Word Count : 126
Differentiate: $f(x)=(x-4)^3(x+1)^2$. By product rule $$ f'(x)= (x-4)^3\cdot 2(x+1)+3(x-4)^2\cdot (x+1)^2 $$ Factor common terms $(x-4)^2(x+1)$: $$ f'(x)=(x-4)^2(x+1)\big(2(x-4)+3(x+1)\big)=5(x-4)^2(x-1)(x+1). $$ Critical points: $x=-1,\,1,\,4$. Note $(x-4)^2$ is nonnegative and has even multiplicity, so the ___ ______ __________ ________ ______ _________ __________ _____ ____ _____.
____ ____ ____ _______ __________.
__________ __________ _____ ________ ______ ___.
________ _______ ______ _______ ______ __________ ___ _________ _______ ________ __________.
____ _____ ____ ________ ___ _________ ____ ________.
________ __________ ___ ____ ________ ___ _____ ___ __________ _____ _________ ____.
__________ ___ _________ _______ _________ ______ _________ ________ ________ ______ ____.
____ ____ __________ ________ _____ __________ ______ ____ ___.
______ ______ ____ ______ _______ __________ _____ ________ ______ __________ _____ __________.
________ __________ ___ _______ _____ ___ ____.
_________ ___ ______ ________.
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Differentiate: $f(x)=(x-4)^3(x+1)^2$. By product rule $$ f'(x)= (x-4)^3\cdot 2(x+1)+3(x-4)^2\cdot (x+1)^2 $$ Factor common terms $(x-4)^2(x+1)$: $$ f'(x)=(x-4)^2(x+1)\big(2(x-4)+3(x+1)\big)=5(x-4)^2(x-1)(x+1). $$ Critical points: $x=-1,\,1,\,4$. Note $(x-4)^2$ is nonnegative and has even multiplicity, so the ___ ______ __________ ________ ______ _________ __________ _____ ____ _____.
____ ____ ____ _______ __________.
__________ __________ _____ ________ ______ ___.
________ _______ ______ _______ ______ __________ ___ _________ _______ ________ __________.
____ _____ ____ ________ ___ _________ ____ ________.
________ __________ ___ ____ ________ ___ _____ ___ __________ _____ _________ ____.
__________ ___ _________ _______ _________ ______ _________ ________ ________ ______ ____.
____ ____ __________ ________ _____ __________ ______ ____ ___.
______ ______ ____ ______ _______ __________ _____ ________ ______ __________ _____ __________.
________ __________ ___ _______ _____ ___ ____.
_________ ___ ______ ________.
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Related Questions
Prove that the set of integers is countable.
जाँच कीजिए :
f (x) = (x-s)3 (x+1)2
द्वारा दिए गए फलन f का स्थानीय उच्चिष्ठ और स्थानीय निम्निष्ठ होता है या नहीं।
Show that
(i)
(ii)
सातत्य की अनुक्रमिक परिभाषा द्वारा सिद्ध कीजिए कि
द्वारा परिभाषित फलन f असतत है, I
State Bonnet's mean value theorem for integrals. Apply it to show that:
Prove that continuous function of a continuous function is continuous.
सिद्ध कीजिए कि
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