Is #f(x)=4x-e^(3x-2) # increasing or decreasing at #x=-2 #?

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Answer 1 · 2016-01-06T21:50:01

#f(x )# is increasing when #x=-2#.

Differentiating the function (chain rule will come into play):

# f'(x ) = 4 - e^(3x - 2 ) . d /dx(3x - 2 ) #

#rArr f'(x ) = 4 - 3e^(3x - 2 ) #

Now evaluate #f'(x )# at #x =- 2 #

# rArr f'( - 2 ) = 4 - 3e^-8 = 4 -3/e^8 = 3.99899361#

Since #f'(-2) > 0# then function is increasing at #x = - 2#.

#f(x)# graphed:

graph{4x-e^(3x-2) [-13.19, 12.12, -6.53, 6.13]}