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The function \[ f(x)= \begin{cases} 2x^2-1, & \text{if } 1 \leq x \leq 4 \\ 151-30x, & \text{if } 4 < x \leq 5 \end{cases} \] is not suitable to apply Rolle's theorem since:
The function \[ f(x)= \begin{cases} 2x^2-1, & \text{if } 1 \leq x \leq 4 \\ 151-30x, & \text{if } 4 < x \leq 5 \end{cases} \] is not suitable to apply Rolle's theorem since:
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Even if a piecewise function "connects" (is continuous), it can still have a "sharp corner" where the slopes don't match. This corner makes it non-differentiable.
Updated On: May 6, 2026
- \( f(x) \) is not continuous on \( [1, 5] \)
- \( f(1) \neq f(5) \)
- \( f(x) \) is continuous only at \( x = 4 \)
- \( f(x) \) is not differentiable in \( (4, 5) \)
- \( f(x) \) is not differentiable at \( x = 4 \)
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