1. Letf be a differentiable function defined on [- 8, 6] . Let f(- 2) = 4 and let flx) have the derivative f "x) ahown. r') a) Use the line tangent to the graph of f at x- -2 to approximate f-2.5). Is this | approximation an over or underestimate? Justify your answer. b) Find the x-coordinate of each point at which the graph of fhas a horizontal tangent line. For each of these points, determine whether f has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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1. Let f be a differentiable function defined on [-8, 6]. Let f(- 2) = 4 and let fix) have the
derivative f (x) shown.
r'(x)
a) Use the line tangent to the graph of f at x = -2 to approximate f(- 2.5). Is this|
approximation an over or underestimate? Justify your answer.
b) Find the x-coordinate of each point at which the graph of fhas a horizontal tangent line. For
each of these points, determine whether f has a relative minimum, relative maximum, or neither
a minimum nor a maximum at the point. Justify your answers.
c) On what interval(s) of x is f both increasing and concave up? Justify your answer.
d) Does the Mean Value Theorem applied on the interval – 8 x6 guarantee a value of c, for
-8<c<6, such that "(e) = . why or why not?
Transcribed Image Text:1. Let f be a differentiable function defined on [-8, 6]. Let f(- 2) = 4 and let fix) have the derivative f (x) shown. r'(x) a) Use the line tangent to the graph of f at x = -2 to approximate f(- 2.5). Is this| approximation an over or underestimate? Justify your answer. b) Find the x-coordinate of each point at which the graph of fhas a horizontal tangent line. For each of these points, determine whether f has a relative minimum, relative maximum, or neither a minimum nor a maximum at the point. Justify your answers. c) On what interval(s) of x is f both increasing and concave up? Justify your answer. d) Does the Mean Value Theorem applied on the interval – 8 x6 guarantee a value of c, for -8<c<6, such that "(e) = . why or why not?
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