Q: Find the critical numbers of f(x)=x^3-2x^2-25x+50

\begin{align}&x=\frac{2+\sqrt{79}}{3}\\&x=\frac{2-\sqrt{79}}{3}\end{align}

Q: Find the local extrema of f(x)=x^3-2x^2-25x+50

\begin{align}&\textrm{The local minimum is}\textrm{ }\frac{884-158\sqrt{79}}{27}\textrm{ }\textrm{at}\textrm{ }x = \frac{2+\sqrt{79}}{3}\\&\textrm{The local maximum is}\textrm{ }\frac{884+158\sqrt{79}}{27}\textrm{ }\textrm{at}\textrm{ }x = \frac{2-\sqrt{79}}{3}\end{align}

Q: Find the increasing or decreasing interval of f(x)=x^3-2x^2-25x+50

\begin{align}&\textrm{The increasing interval is}\textrm{ }x \in \left(-\infty,\frac{2-\sqrt{79}}{3}\right]\cup \left[\frac{2+\sqrt{79}}{3},+\infty\right)\\&\textrm{The decreasing interval is}\textrm{ }\frac{2-\sqrt{79}}{3}\leq x\leq \frac{2+\sqrt{79}}{3}\end{align}

Q: Find the vertical asymptotes of f(x)=x^3-2x^2-25x+50

\textrm{No vertical asymptotes}

Q: Find the horizontal asymptotes of f(x)=x^3-2x^2-25x+50

\textrm{No horizontal asymptotes}

Q: Testing for symmetry about the origin of f(x)=x^3-2x^2-25x+50

\textrm{Not symmetry with respect to the origin}

Q: Testing for symmetry about the x-axis of f(x)=x^3-2x^2-25x+50

\textrm{Not symmetry with respect to the x-axis}

Question 1

Evaluate the derivative of f(x)=x^3-2x^2-25x+50

Accepted Answer

f^{\prime}\left(x\right)=3x^{2}-4x-25

Question 2

Find the domain of f(x)=x^3-2x^2-25x+50

Accepted Answer

x \in \mathbb{R}

Question 3

ext{Find the }x	ext{-intercept/zero} of f(x)=x^3-2x^2-25x+50

Accepted Answer

x_{1}=-5,x_{2}=2,x_{3}=5

Question 4

Find the y-intercept of f(x)=x^3-2x^2-25x+50

Accepted Answer

f\left(0\right)=50

Question 5

Find the critical numbers of f(x)=x^3-2x^2-25x+50

Accepted Answer

\begin{align}&x=\frac{2+\sqrt{79}}{3}\&x=\frac{2-\sqrt{79}}{3}\end{align}

Question 6

Find the local extrema of f(x)=x^3-2x^2-25x+50

Accepted Answer

\begin{align}& extrm{The local minimum is} extrm{ }\frac{884-158\sqrt{79}}{27} extrm{ } extrm{at} extrm{ }x = \frac{2+\sqrt{79}}{3}\& extrm{The local maximum is} extrm{ }\frac{884+158\sqrt{79}}{27} extrm{ } extrm{at} extrm{ }x = \frac{2-\sqrt{79}}{3}\end{align}

Question 7

Find the increasing or decreasing interval of f(x)=x^3-2x^2-25x+50

Accepted Answer

\begin{align}& extrm{The increasing interval is} extrm{ }x \in \left(-\infty,\frac{2-\sqrt{79}}{3} ight]\cup \left[\frac{2+\sqrt{79}}{3},+\infty ight)\& extrm{The decreasing interval is} extrm{ }\frac{2-\sqrt{79}}{3}\leq x\leq \frac{2+\sqrt{79}}{3}\end{align}

Question 8

Find the range of f(x)=x^3-2x^2-25x+50

Accepted Answer

f\left(x\right) \in \mathbb{R}

Question 9

Find the vertical asymptotes of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{No vertical asymptotes}

Question 10

Find the horizontal asymptotes of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{No horizontal asymptotes}

Question 11

Find the oblique asymptotes of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{No oblique asymptotes}

Question 12

Determine if even, odd or neither of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{Neither even nor odd}

Question 13

Find the stationary points of f(x)=x^3-2x^2-25x+50

Accepted Answer

\left(\frac{2-\sqrt{79}}{3},\frac{884+158\sqrt{79}}{27}\right),\left(\frac{2+\sqrt{79}}{3},\frac{884-158\sqrt{79}}{27}\right)

Question 14

Find the inflection points of f(x)=x^3-2x^2-25x+50

Accepted Answer

\begin{align}&\left(\frac{2}{3},\frac{884}{27}\right)\end{align}

Question 15

Testing for symmetry about the origin of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{Not symmetry with respect to the origin}

Question 16

Testing for symmetry about the x-axis of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{Not symmetry with respect to the x-axis}

Question 17

Testing for symmetry about the y-axis of f(x)=x^3-2x^2-25x+50

Accepted Answer

extrm{Not symmetry with respect to the y-axis}

f(x)=x^3-2x^2-25x+50

Function

Testing for symmetry

Graph

Frequently Asked Questions

Evaluate the derivative of \(f(x)=x^3-2x^2-25x+50\)

Find the domain of \(f(x)=x^3-2x^2-25x+50\)

$Find the x -intercept/zero$ of \(f(x)=x^3-2x^2-25x+50\)

Find the y-intercept of \(f(x)=x^3-2x^2-25x+50\)

Find the critical numbers of \(f(x)=x^3-2x^2-25x+50\)

Find the local extrema of \(f(x)=x^3-2x^2-25x+50\)

Find the increasing or decreasing interval of \(f(x)=x^3-2x^2-25x+50\)

Find the range of \(f(x)=x^3-2x^2-25x+50\)

Find the vertical asymptotes of \(f(x)=x^3-2x^2-25x+50\)

Find the horizontal asymptotes of \(f(x)=x^3-2x^2-25x+50\)

Find the oblique asymptotes of \(f(x)=x^3-2x^2-25x+50\)

Determine if even, odd or neither of \(f(x)=x^3-2x^2-25x+50\)

Find the stationary points of \(f(x)=x^3-2x^2-25x+50\)

Find the inflection points of \(f(x)=x^3-2x^2-25x+50\)

Testing for symmetry about the origin of \(f(x)=x^3-2x^2-25x+50\)

Testing for symmetry about the x-axis of \(f(x)=x^3-2x^2-25x+50\)

Testing for symmetry about the y-axis of \(f(x)=x^3-2x^2-25x+50\)