Let f be a continuous positive function on the interval [a, b]. Assume f= F'. Explain what each of the following expressions represents on the indicated graph. Pay close attention to the notation. (a) F(b) F(a) on the graph of f. O The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to f at x = a. O The change in f from x = a to x = b. O The area under the secant line between the points (a, f(a)) and (b, f(b)). O The area under the curve y = f(x) on the interval [a, b]. O The slope of the secant line between the points (a, f(a)) and (b, f(b)). O The slope of the tangent line to fat x = a. O The average value of f over the interval [a, b]. fºfex on the graph of F. b-a O The difference between the slope of the tangent line to F at x = b and the slope of the tangent line to F at x = a. (b) f(x)dx O The change in F from x = a to x = b. O The area under the secant line between the points (a, F(a)) and (b, F(b)). O The area under the curve y = F(x) on the interval [a, b]. O The slope of the secant line between the points (a, F(a)) and (b, F(b)). O The slope of the tangent line to F at x = a. O The average value of F over the interval [a, b]. (c) ["f f(x) dx on the graph of f. b-a O The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to fat x = a. O The change in f from x = a to x = b. O The area under the secant line between the points (a, f(a)) and (b, f(b)). O The area under the curve y = f(x) on the interval [a, b]. O The slope of the secant line between the points (a, f(a)) and (b, f(b)). O The slope of the tangent line to f at x = a. O The average value of f over the interval [a, b].
Let f be a continuous positive function on the interval [a, b]. Assume f= F'. Explain what each of the following expressions represents on the indicated graph. Pay close attention to the notation. (a) F(b) F(a) on the graph of f. O The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to f at x = a. O The change in f from x = a to x = b. O The area under the secant line between the points (a, f(a)) and (b, f(b)). O The area under the curve y = f(x) on the interval [a, b]. O The slope of the secant line between the points (a, f(a)) and (b, f(b)). O The slope of the tangent line to fat x = a. O The average value of f over the interval [a, b]. fºfex on the graph of F. b-a O The difference between the slope of the tangent line to F at x = b and the slope of the tangent line to F at x = a. (b) f(x)dx O The change in F from x = a to x = b. O The area under the secant line between the points (a, F(a)) and (b, F(b)). O The area under the curve y = F(x) on the interval [a, b]. O The slope of the secant line between the points (a, F(a)) and (b, F(b)). O The slope of the tangent line to F at x = a. O The average value of F over the interval [a, b]. (c) ["f f(x) dx on the graph of f. b-a O The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to fat x = a. O The change in f from x = a to x = b. O The area under the secant line between the points (a, f(a)) and (b, f(b)). O The area under the curve y = f(x) on the interval [a, b]. O The slope of the secant line between the points (a, f(a)) and (b, f(b)). O The slope of the tangent line to f at x = a. O The average value of f over the interval [a, b].
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![Let f be a continuous positive function on the interval [a, b]. Assume f = F'. Explain what each of the following expressions represents on the indicated graph. Pay close attention to the notation.
(a) F(b) - F(a) on the graph of f.
O The difference between the slope of the tangent line to fat x = b and the slope of the tangent line to f at x = a.
O The change in f from x = a to x = b.
O The area under the secant line between the points (a, f(a)) and (b, f(b)).
O The area under the curve y = f(x) on the interval [a, b].
O The slope of the secant line between the points (a, f(a)) and (b, f(b)).
The slope of the tangent line to fat x = a.
O The average value of f over the interval [a, b].
(b) f(x)dx
Tº FC
b-a
The difference between the slope of the tangent line to F at x = b and the slope of the tangent line to F at x = a.
The change in F from x = a to x = b.
O The area under the secant line between the points (a, F(a)) and (b, F(b)).
O The area under the curve y = F(x) on the interval [a, b].
The slope of the secant line between the points (a, F(a)) and (b, F(b)).
O The slope of the tangent line to F at x = a.
The average value of F over the interval [a, b].
(c)
on the graph of F.
f(x) dx
on the graph of f.
b-a
The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to fat x = a.
O The change in f from x = a to x = b.
The area under the secant line between the points (a, f(a)) and (b, f(b)).
O The area under the curve y = f(x) on the interval [a, b].
O The slope of the secant line between the points (a, f(a)) and (b, f(b)).
The slope of the tangent line to fat x = a.
O The average value of f over the interval [a, b].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb7caee6-5e20-4b18-a410-4355893eb850%2F77520e3e-5b6e-4c72-8375-312a66cbffea%2F1k8dsb6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f be a continuous positive function on the interval [a, b]. Assume f = F'. Explain what each of the following expressions represents on the indicated graph. Pay close attention to the notation.
(a) F(b) - F(a) on the graph of f.
O The difference between the slope of the tangent line to fat x = b and the slope of the tangent line to f at x = a.
O The change in f from x = a to x = b.
O The area under the secant line between the points (a, f(a)) and (b, f(b)).
O The area under the curve y = f(x) on the interval [a, b].
O The slope of the secant line between the points (a, f(a)) and (b, f(b)).
The slope of the tangent line to fat x = a.
O The average value of f over the interval [a, b].
(b) f(x)dx
Tº FC
b-a
The difference between the slope of the tangent line to F at x = b and the slope of the tangent line to F at x = a.
The change in F from x = a to x = b.
O The area under the secant line between the points (a, F(a)) and (b, F(b)).
O The area under the curve y = F(x) on the interval [a, b].
The slope of the secant line between the points (a, F(a)) and (b, F(b)).
O The slope of the tangent line to F at x = a.
The average value of F over the interval [a, b].
(c)
on the graph of F.
f(x) dx
on the graph of f.
b-a
The difference between the slope of the tangent line to f at x = b and the slope of the tangent line to fat x = a.
O The change in f from x = a to x = b.
The area under the secant line between the points (a, f(a)) and (b, f(b)).
O The area under the curve y = f(x) on the interval [a, b].
O The slope of the secant line between the points (a, f(a)) and (b, f(b)).
The slope of the tangent line to fat x = a.
O The average value of f over the interval [a, b].
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