Is #f(x)=1/sqrt(x+3) # increasing or decreasing at #x=3 #?

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Answer 1 · 2016-01-07T19:15:07

decreasing

to test if the function is increasing or decreasing we require to differentiate it and then test if it's value at x = 3 is > 0 or < 0.

# f(x) = 1/sqrt(x + 3 ) = (x + 3 )^(-1/2) #

# rArr f'(x) = -1/2 (x + 3 )^-(3/2) #

#rArr f'(x) = -1/(x + 3 )^(3/2 #

at x = 3 : # f'(3) = -1 /(3 + 3) ^(3/2) #

which will be < 0 # AAx #

since f'(3) < 0 the function f(x) is decreasing at x = 3

graph{(x + 3)^-1/2 [-10, 10, -5, 5]}