Question

Verify that Rolle's Theorem can be applied to the function \( f(x)=x^{3}-13 x^{2}+50 x-56 \) on the interval \( [2,7] \). Then find all values of \( c \) in the interval such that \( f^{\prime}(c)=0 \). Enter the exact answers in increasing order. To enter \( \sqrt{a} \), type sqrt(a). \[ \begin{array}{l} c=\square \text { ? } \frac{\Delta}{\Sigma} \\ c=\square \text { ? } \frac{\Delta}{\Sigma} \end{array} \] Show your work and explain, in your own words, how you arrived at your answers.

          Verify that Rolle's Theorem can be applied to the function \( f(x)=x^{3}-13 x^{2}+50 x-56 \) on the interval \( [2,7] \). Then find all values of \( c \) in the interval such that \( f^{\prime}(c)=0 \).

Enter the exact answers in increasing order.

To enter \( \sqrt{a} \), type sqrt(a).
\[
\begin{array}{l}
c=\square \text { ? } \frac{\Delta}{\Sigma} \\
c=\square \text { ? } \frac{\Delta}{\Sigma}
\end{array}
\]

Show your work and explain, in your own words, how you arrived at your answers.

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Verify that Rolle's Theorem can be applied to the function f(x)=x^3-13 x^2+50 x-56 on the interval [2,7]. Then find all values of c in the interval such that f^'(c)=0.

Enter the exact answers in increasing order.

To enter √(a), type sqrt(a).

c=□ ? (Δ)/(Σ)

c=□ ? (Δ)/(Σ)

Show your work and explain, in your own words, how you arrived at your answers.

Added by Nathan S.

Calculus

Laura Taalman, Peter Kohn 1st Edition

Chapter 3

Instant Answer

Solved by Expert Sri K

08/09/2023

Step 1

Rolle's Theorem states that if a function \( f \) is continuous on a closed interval \([a, b]\), differentiable on the open interval \((a, b)\), and \( f(a) = f(b) \), then there exists at least one \( c \) in \((a, b)\) such that \( f'(c) = 0 \). 1. Show more…

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Verify that Rolle's Theorem can be applied to the function \( f(x)=x^{3}-13 x^{2}+50 x-56 \) on the interval \( [2,7] \). Then find all values of \( c \) in the interval such that \( f^{\prime}(c)=0 \). Enter the exact answers in increasing order. To enter \( \sqrt{a} \), type sqrt(a). \[ \begin{array}{l} c=\square \text { 回 } \frac{\Delta}{\Sigma} \\ c=\square \text { 回 } \frac{\Delta}{\Sigma} \end{array} \] Show your work and explain, in your own words, how you arrived at your answers.

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