Applications of Derivatives · Local maxima and minima

Let

f

be a differentiable function satisfying

f(x) = 1 - 2x + \int_0^x e^{(x-t)}f(t)\,dt,\ x \in \mathbb{R}

and let

g(x) = \int_0^x (f(t) + 2)^{15}(t - 4)^6(t + 12)^{17}\,dt,\ x \in \mathbb{R}.

p

and

q

are respectively the points of local minima and local maxima of

g

, then the value of

\lvert p + q\rvert

is equal to .

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