4. Consider the functions below. (i) Determine and explain whether the Mean Value Theorem applies to the function on the given interval. (ii) If MVT applies, find the exact point(s) that are guaranteed to exist. (iii) If MVT applies, make a sketch of the function and the line passing through the end points of the given interval. Sketch the point P which exists by MVT. Sketch the line tangent to the function at P with the same slope as the secant line through the endpoints. (a) f(x) = |x – 1| on [-1,4] (b) g(x) = x-1/3 on 8

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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4. Consider the functions below. (i) Determine and explain whether the Mean Value Theorem
applies to the function on the given interval. (ii) If MVT applies, find the exact point(s) that are
guaranteed to exist. (iii) If MVT applies, make a sketch of the function and the line passing
through the end points of the given interval. Sketch the point P which exists by MVT. Sketch the
line tangent to the function at P with the same slope as the secant line through the endpoints.
(a) f(x) = |x – 1| on [-1,4]
(b) g(x) = x-1/3 on ,8]
Transcribed Image Text:4. Consider the functions below. (i) Determine and explain whether the Mean Value Theorem applies to the function on the given interval. (ii) If MVT applies, find the exact point(s) that are guaranteed to exist. (iii) If MVT applies, make a sketch of the function and the line passing through the end points of the given interval. Sketch the point P which exists by MVT. Sketch the line tangent to the function at P with the same slope as the secant line through the endpoints. (a) f(x) = |x – 1| on [-1,4] (b) g(x) = x-1/3 on ,8]
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