Use your results to write the complete factorization of f(x). Function f(x) = 2x^3 - x^2 - 10x + 5 Factors (2x - 1), (x + sqrt5)

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Use your results to write the complete factorization of f(x). Function f(x) = 2x^3 - x^2 - 10x + 5 Factors (2x - 1), (x + sqrt5)

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asked 2021-03-20

The graph of y = f(x) contains the point (0,2), \(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\frac{{-{x}}}{{{y}{e}^{{{x}^{{2}}}}}}}\), and f(x) is greater than 0 for all x, then f(x)=
A) \(\displaystyle{3}+{e}^{{-{x}^{{2}}}}\)
B) \(\displaystyle\sqrt{{{3}}}+{e}^{{-{x}}}\)
C) \(\displaystyle{1}+{e}^{{-{x}}}\)
D) \(\displaystyle\sqrt{{{3}+{e}^{{-{x}^{{2}}}}}}\)
E) \(\displaystyle\sqrt{{{3}+{e}^{{{x}^{{2}}}}}}\)

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asked 2021-02-21

Use the piecewise-defined function to fill in the bla
.
\(\displaystyle{f{{\left({x}\right)}}}={\left\lbrace{4},-{4}{<}{x}{<}-{2},{2}{x}-{4},-{1}{<}{x}{<}{2},{3}{x},{2}\le{x}{<}{5}\right\rbrace}\)
a. The domain ____ is used when graphing the function \(f(x)=2x-4\).
b. The equation ____ is used to find \(f(4)=12.\)

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asked 2021-06-01

Use the theorems on derivatives to find the derivatives of the following function:
\(\displaystyle{f{{\left({x}\right)}}}={\left({5}{x}^{{{3}}}+{8}{x}^{{{2}}}-{4}\right)}^{{{4}}}{\left({8}{x}^{{{4}}}-{2}{x}^{{{3}}}-{7}\right)}\)

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asked 2021-05-07

Find f'(a)
\(\displaystyle{f{{\left({t}\right)}}}={\frac{{{3}{t}+{3}}}{{{t}+{2}}}}\)

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asked 2021-01-27

Suppose that f(x) is a continuous, one-to-one function such that \(\displaystyle{f{{\left({2}\right)}}}={1},{f}'{\left({2}\right)}=\frac{{1}}{{4}},{f{{\left({1}\right)}}}={3}\), and f '(1) = 7. Let \(\displaystyle{g{{\left({x}\right)}}}={{f}^{{−{1}}}{\left({x}\right)}}\) and let \(\displaystyle{G}{\left({x}\right)}={x}^{{2}}\cdot{g{{\left({x}\right)}}}\). Find G'(1). (You may not need to use all of the provided information.)

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asked 2021-05-04

Use the theorems on derivatives to find the derivatives of the following function:
\(\displaystyle{f{{\left({x}\right)}}}={3}{x}^{{{5}}}-{2}{x}^{{{4}}}-{5}{x}+{7}+{4}{x}^{{-{2}}}\)

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asked 2021-01-31

A canyon is 900 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.) How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.)

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asked 2020-11-11

Use exponential regression to find a function that models the data. \(\begin{array}{|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 \\ \hline f(x) & 14 & 7.1 & 3.4 & 1.8 & 0.8 \\ \hline \end{array}\)

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asked 2021-01-13

Evaluate the piecewise defined function at the indicated values.
\(a^m inH\)
\(f(x)= \begin{array}{11}{5}&\text{if}\ x \leq2 \ 2x-3& \text{if}\ x>2\end{array}\)
\(a^m inH\)
f(-3),f(0),f(2),f(3),f(5)

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asked 2021-03-09

The function given by \(\displaystyle{f{{\left({x}\right)}}}=−{3}{x}^{{5}}+√{2}{x}+\frac{{1}}{{2}}{x}\) (is/is not) a polynomial function.

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Answer 1

Use part b to write the complete factorization.
\(\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{3}}-{x}^{{2}}-{10}{x}+{5}\)
\(\displaystyle={\left({2}{x}-{1}\right)}{\left({x}+\sqrt{{5}}\right)}{\left({x}-\sqrt{-}{5}\right)}\)

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Use your results to write the complete factorization of f(x). Function f(x) = 2x^3 - x^2 - 10x + 5 Factors (2x - 1), (x + sqrt5)

Use your results to write the complete factorization of f(x). Function f(x) = 2x^3 - x^2 - 10x + 5 Factors (2x - 1), (x + sqrt5)

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