Writing If p(x) is a polynomial, discuss the usefulnessof knowing zeros for p, p, and p

Chapter 4, Problem 84

(choose chapter or problem)

Let $f(x)=(x-2)^{2} e^{x / 2}$. Given that

$f^{\prime}(x)=\frac{1}{2}\left(x^{2}-4\right) e^{x / 2}, \quad f^{\prime \prime}(x)=\frac{1}{4}\left(x^{2}+x 4-4\right) e^{x / 2}$

determine the following properties of the graph of $f$.

(a) The horizontal asymptote is _______.

(b) The graph is above the $x$-axis on the intervals _______.

(d) The graph is concave up on the intervals _______.

(e) The relative minimum point on the graph is _______.

(f ) The relative maximum point on the graph is _______.

(g) Inflection points occur at $x =$ _______.

Equation Transcription:

$f(x)=(x-2{)}^{2}{e}^{x/2}$

$f'(x)=\ \frac{1}{2}({x}^{2}-4){e}^{x/2},\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ f"(x)=\frac{1}{4}({x}^{2}+x4-4){e}^{x/2}$

$f$

$x$

$x=$

Text Transcription:

f(x) = (x − 2)^2e^x/2.

f’ (x) = 1/2 (x^2 − 4)e^x/2, f” (x) = 1/4 (x^2 + 4x − 4)e^x/2

x =

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