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# 3 10 pts a let f x e x 3 x show that f is one to one

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3. (10 pts.) (a) Let f ( x ) e x 3 x Show that f is one-to-one on using f . [A little explanation is needed!] (b) Suppose that a one-to-one function f has a tangent line given by y = 5 x + 3 at the point (1,8). Find f -1 (8) and ( f -1 ) (8). f 1 (8) ( f 1 ) (8) ______________________________________________________________________ 4. (10 pts.) Write down each of the following derivatives. [2 pts/part.] (a) d [tan 1 ] dx ( x ) (b) d [sin 1 ] dx ( x ) (c) d [ csc 1 ] dx ( x ) (d) d [cos 1 ] dx ( x ) (e) d [cot 1 ] dx ( x )

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TEST3/MAC2311 Page 3 of 5 ______________________________________________________________________ 5. (10 pts.) Fill in the blanks appropriately. [DEFINITIONS!!!] (a) A function f has a relative maximum at x 0 if there is an open interval containing x 0 on which for each x in both the interval and the domain of f . (b) A function f is concave down on an interval ( a , b ) if the derivative of f is on ( a , b ). (c) A function f is concave up on an interval ( a , b ) if the derivative of f is on ( a , b ). (d)
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3 10 pts a Let f x e x 3 x Show that f is one to one on...

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