In Exercises 89–92, let for the specified a, u, and ƒ. Use

Chapter 5, Problem 89CE

(choose chapter or problem)

In Exercises , let \(F(x)=\int_{a}^{2(x)} f(t) d t\) for the specified \(a\), \(u\), and \(f\). Use a CAS to perform the following steps and answer the questions posed.

a. Find the domain of \(F\).

b. Calculate \(F^{\prime}(x)\) and determine its zeros. For what points in its domain is \(F\) increasing? Decreasing?

c. Calculate \(F^{\prime \prime}(x)\) and determine its zero. Identify the local extrema and the points of inflection of \(F\).

d. Using the information from parts (a)-(c), draw a rough hand sketch of \(y=F(x)\) over its domain. Then graph \(F(x)\) on your CAS to support your sketch.

\(a=1,\ \ \ u(x)=x^2,\ \ \ f(x)=\sqrt{1-x^2}\)

Equation  Transcription:

Text Transcription:

F(x)= integral a 2(x) f (t)dt

a

u

f

F

F'(x)

F''(x)

y=f(x)

F(x)

a=1, u(x)=x^2, f(x)  = square root 1-x^2