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

1 Answer
Jan 6, 2016

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

Explanation:

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]}