- #1

karush

Gold Member

MHB

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Let $g(x)$ be the function given by $g(x) = x^2e^{kx}$ , where k is a constant. For what value of k does g have a critical point at $x=\dfrac{2}{3}$?

$$(A)\quad {-3}

\quad (B)\quad -\dfrac{3}{2}

\quad (C)\quad -\dfrac{3}{2}

\quad (D)\quad {0}

\quad (E)\text{ There is no such k}$$

ok I really did not know how you could isolate k to solve this.

if you plug in $x=\dfrac{2}{3}$ then g(2/3)

if you plug in $x=\dfrac{2}{3}$ then $g(2/3)=\dfrac{4}{9}e^\dfrac{2k}{3}$

$$(A)\quad {-3}

\quad (B)\quad -\dfrac{3}{2}

\quad (C)\quad -\dfrac{3}{2}

\quad (D)\quad {0}

\quad (E)\text{ There is no such k}$$

ok I really did not know how you could isolate k to solve this.

if you plug in $x=\dfrac{2}{3}$ then g(2/3)

if you plug in $x=\dfrac{2}{3}$ then $g(2/3)=\dfrac{4}{9}e^\dfrac{2k}{3}$

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