5. Let f(t)= te-2t and F(x) = f f(t) dt. a. Determine F'(x). b. Use the First FTC to find a formula for F that does not involve an integral. c. Is F an increasing or decreasing function for x > 0? Why?

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.
Chapter5: Graphs And The Derivative
Section5.3: Higher Derivatives, Concavity, And The Second Derivative Test
Problem 30E
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5. Let f(t)= te-2t and F(x) = f f(t) dt.
a. Determine F'(x).
b. Use the First FTC to find a formula for F that does not involve an integral.
c. Is F an increasing or decreasing function for x > 0? Why?
Transcribed Image Text:5. Let f(t)= te-2t and F(x) = f f(t) dt. a. Determine F'(x). b. Use the First FTC to find a formula for F that does not involve an integral. c. Is F an increasing or decreasing function for x > 0? Why?
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