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Activity9.3Formal Identification of Critical Numbers

When finding critical numbers based upon a function formula, there are three issues that need to be considered; the domain of the function, the zeros of the first derivative, and the numbers in the domain of the function where the first derivative is undefined. When writing a formal analysis of this process each of these questions must be explicitly addressed. The following outline shows the work you need to show when you are asked to write a formal determination of critical numbers based upon a function formula.

Subsection9.3.1Exercises

Formally establish the critical numbers for each of the following functions following the procedure outlined in Algorithm 9.3.1.

1

f(x)=x29x+4

2

g(t)=7t3+39t224t

3

p(t)=(t+8)23

4

z(x)=xln(x)

5

y(θ)=ecos(θ)

6

T(t)=t416t

The first derivative of the function m(x)=x5x7 is

m(x)=3x2x5(x7)2.
7

Roland says that 5 is a critical number of m but Yuna disagrees. Who is correct and why?

8

Roland says that 7 is a critical number of m but Yuna disagrees. Who is correct and why?

9

Roland says that 3 is a critical number of m but Yuna disagrees. Who is correct and why?