For the function f (x) whose graph is given on (0,10.5) a) Estimate: f \'(1) ? _

Question

For the function f (x) whose graph is given on (0,10.5)

a) Estimate:

f '(1) ? _____

f '(3) ? _____

f '(7) ? _____

f '(8) ? _____

f '(9) ? _____

b.) Find if exists; if not, write DNE:

f(x) has local maximum value(s) at x = ________________________________________

f(x) has global minimum value (s) at x = _________________________________________

f(x) is increasing on the interval (s) ___________________________________________

f'(x) < 0 on the interval (s) _________________________________________________

f''(x) > 0 on the interval (s) _________________________________________________

f is concave down on the interval (s) _________________________________________

For the function f(x) whose graph is given on (0,10.5) Estimate: f '(1) ? f '(3) ? f '(7) ? f '(8) ? f '(9) ? Find if exists; if not, write DNE: f(x) has local maximum value(s) at x = f(x) has global minimum value (s) at x = f(x) is increasing on the interval (s) f'(x) 0 on the interval (s) f is concave down on the interval (s)

Explanation / Answer

a)

f'(1)=(7-1)/(0-2)=-3

f'(3)=0

the parabola curve is y=7-(x-8)^2

so

y'=-2(x-8)

so

f'(7)=2

f'(8)=0

f'(9)=-2

b)

local max at x=8

global min at x=8+sqrt(7)

inc in [4,8]

f'(x)<0 i.e dec in [0,2] U [8,8+sqrt(7)]

f''(x)>0 in no interval

concave down in [6,8+sqrt(7)]

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