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

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Answer 1 · 2016-01-06T21:50:01

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

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]}

Is f(x)=4x-e^(3x-2) f(x)=4x−e3x−2f(x)=4x-e^(3x-2) increasing or decreasing at x=-2 x=−2x=-2 ?