Solved: Critical points of functions with unknown

Chapter 7, Problem 57E

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QUESTION:

56–59. Critical points of functions with unknown parameters Find the critical points of f. Assume a and b are constants.

\(f(x)=x \sqrt{x-a}\)

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QUESTION:

56–59. Critical points of functions with unknown parameters Find the critical points of f. Assume a and b are constants.

\(f(x)=x \sqrt{x-a}\)

ANSWER:

Solution 57E Step-1 Critical value definition ; Let f be a continuous function defined on an open interval containing a 1 number ‘c’.The number ‘c’ is critical value ( or critical number ). If f (c) = 0 or f (c) is undefined. A critical point on that graph of f has the form (c,f(c)). Step-2 a). The given function is f(x) = xx a . Clearly the function contains the root value So , x - a 0 That is , x a Therefore , x belongs to [a, ) Therefore, the given funct

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