* x f(x) f'(x) 1 3 1 2 -1 3 3 3 3 5 -2 4 -2 4 5 4 -2 The table above gives values of f and its derivative f' at selected values of x. The function f is twice differentiable at all x. (a) Use the values in the table to estimate the value of f'(1.5). (b) Explain why there must be a value c for 1

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 54CR
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*
x
f(x) f'(x)
1
3
1
2
-1
3
3
3
3
5
-2
4 -2
4
5
4
-2
The table above gives values of f and its derivative f' at selected
values of x. The function f is twice differentiable at all x.
(a) Use the values in the table to estimate the value of f'(1.5).
Transcribed Image Text:* x f(x) f'(x) 1 3 1 2 -1 3 3 3 3 5 -2 4 -2 4 5 4 -2 The table above gives values of f and its derivative f' at selected values of x. The function f is twice differentiable at all x. (a) Use the values in the table to estimate the value of f'(1.5).
(b) Explain why there must be a value c for 1 <c<3, for
which f'(c) = 1.
(c) Estimate the average value of f(x) from 1 ≤ x ≤ 4 using
a trapezoidal sum with 3 subintervals, as indicated in the
table.
(d) Assuming f is invertible, find the equation of the line
tangent to the graph of y = f(x) at x = 5.
Transcribed Image Text:(b) Explain why there must be a value c for 1 <c<3, for which f'(c) = 1. (c) Estimate the average value of f(x) from 1 ≤ x ≤ 4 using a trapezoidal sum with 3 subintervals, as indicated in the table. (d) Assuming f is invertible, find the equation of the line tangent to the graph of y = f(x) at x = 5.
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