Survey of Calculus Test 2
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Find the x coordinates of all relative extreme points of[pic].
|A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] |
[pic]
First find the derivative of the function[pic], f ’(x):
|[pic] |= |[pic] |apply power rule of differentiation |
| |= |[pic] |simplify |
| |= |[pic] |finish simplifying by first factoring |
| | | |out GCF |
| |= |[pic] |next factor the trinomial factor, |
| | | |leaving the final simplified form of |
| | | |the derivative |
Set[pic]and solve for x to find critical point(s):
When the derivative is set to zero, [pic]; thus, this implies each factor could be equal to zero, meaning that there could be up to three values for x.
|[pic] |= |[pic] |set first factor equal to zero |
|[pic] |= |[pic] |divide each side of the equation by 2|
|[pic] |= |[pic] |simplify to find first value of x |
|[pic] |= |[pic]
|A)[pic] |B) [pic] |C) [pic] |D) [pic] |E) [pic] |
[pic]
First find the derivative of the function[pic], f ’(x):
|[pic] |= |[pic] |apply power rule of differentiation |
| |= |[pic] |simplify |
| |= |[pic] |finish simplifying by first factoring |
| | | |out GCF |
| |= |[pic] |next factor the trinomial factor, |
| | | |leaving the final simplified form of |
| | | |the derivative |
Set[pic]and solve for x to find critical point(s):
When the derivative is set to zero, [pic]; thus, this implies each factor could be equal to zero, meaning that there could be up to three values for x.
|[pic] |= |[pic] |set first factor equal to zero |
|[pic] |= |[pic] |divide each side of the equation by 2|
|[pic] |= |[pic] |simplify to find first value of x |
|[pic] |= |[pic]