# Question Need hep with both of these math problems from my homework!     AND   Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)

Need hep with both of these math problems from my homework!

AND

Transcribed Image Text: Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
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Transcribed Image Text: Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) Determine the intervals on which the function is concave up or down and find the points of inflection. $f(x)=2 x^{3}-7 x^{2}+6$ (Give your answer as a comma-separated list of points in the form ( $$\left.{ }^{*},{ }^{*}\right)$$. Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which $$f$$ is concave up. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right.$$ ). Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) $x \in$ Determine the interval on which $$f$$ is concave down. (Give your answer as an interval in the form $$\left({ }^{*},{ }^{*}\right)$$. Use the symbol $$\infty$$ for infinity, $$\cup$$ for combining intervals, and an appropriate type of parenthesis "("," ")", "[","]" depending on whether the interval is open or closed. Enter $$\varnothing$$ if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.)
&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/1Solution: Function given as $$\mathrm{{f{{\left({x}\right)}}}={2}{x}^{{3}}-{7}{x}^{{2}}+{6}}$$For point of inflection f''(x) = 0 $$\mathrm{{f}'{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}\right.}}{\left({2}{x}^{{3}}-{7}{x}^{{2}}+{6}\right)}}$$$$\mathrm{{f}'{\left({x}\right)}={6}{x}^{{2}}-{14}{x}}$$Again, $$\mathrm{{f}{''}{\left({x}\right)}=\frac{{d}}{{\left.{d}{x}\right.}}{\left({6}{x}^{{2}}-{14}{x}\right)}\Rightarrow{12}{x}-{14}}$$For point of inflection f''(x) = 0 \( \mathrm ... See the full answer