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The second derivative of a function
h is given by
h^('')(x)=(root(3)(x))/(e^(x))+1.
Where does the graph of
h have a point of inflection?
Use a graphing calculator.
Choose 1 answer:
(A)
x=-0.35
(B)
x=0
(C)
x=0.33
(D)
x=1.497

The second derivative of a function $h$ is given by $h^{\prime \prime}(x)=\frac{\sqrt[3]{x}}{e^{x}}+1$ . $\newline$ Where does the graph of $h$ have a point of inflection? $\newline$ Use a graphing calculator. $\newline$ Choose $1$ answer: $\newline$ (A) $x=-0.35$ $\newline$ (B) $x=0$ $\newline$ (C) $x=0.33$ $\newline$ (D) $x=1.497$

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Find higher derivatives of rational and radical functions

Full solution

Q. The second derivative of a function

h

is given by

h^{\prime \prime}(x)=\frac{\sqrt[3]{x}}{e^{x}}+1

.

\newline

Where does the graph of

h

have a point of inflection?

\newline

Use a graphing calculator.

\newline

Choose

1

answer:

\newline

(A)

x=-0.35

\newline

(B)

x=0

\newline

(C)

x=0.33

\newline

(D)

x=1.497

Set Second Derivative Equal: To find the point of inflection, we need to set the second derivative equal to zero and solve for $x$ . $h''(x) = \frac{\sqrt[3]{x}}{e^{x}} + 1 = 0$
Use Graphing Calculator: We use a graphing calculator to find the value of $x$ where $h''(x) = 0$ .
Find $X$ -Value: After plotting the function $h''(x)$ on the graphing calculator, we look for the $x$ -value where the graph crosses the $x$ -axis.
Crosses X-Axis: The graph crosses the x-axis near $x = 1.497$ , which corresponds to answer choice (D).

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