Find the value c guaranteed by the mean value theorem for \(f(x)=x^{2}-4x\) on \([0,4]\).

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Review the concept: Mean value theorem

If \(f\) is continuous on \([a,b]\) and differentiable on \((a,b)\), there is a \(c\in(a,b)\) such that the slope of the tangent at \(c\) equals the slope of the secant line joining \((a,f(a))\) and \((b,f(b))\).

More practice problems: mean value theorem

• ZW-MEAN-VALUE-THEOREM-001 Find the value c guaranteed by the mean value theorem for f(x)=x^2 on [1,3].
• ZW-MEAN-VALUE-THEOREM-002 Find the value c guaranteed by the mean value theorem for f(x)=x^3 on [0,2].
• ZW-MEAN-VALUE-THEOREM-003 Find the value c guaranteed by the mean value theorem for f(x)=√x on [1,4].
• ZW-MEAN-VALUE-THEOREM-004 Which hypothesis does the mean value theorem require for f on [a,b]?
• ZW-MEAN-VALUE-THEOREM-005 Compute the slope of the secant line of f(x)=x^3 between x=1 and x=2.
• ZW-MEAN-VALUE-THEOREM-006 According to the mean value theorem, what slope must the tangent at the point c have?
• ZW-MEAN-VALUE-THEOREM-008 Find the value c guaranteed by the mean value theorem for f(x)=x^3-3x on [0,2].
• ZW-MEAN-VALUE-THEOREM-009 If f'(x)=0 for all x in (a,b) and f is continuous on [a,b], what can be said about f?

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