Central and peripheral route dilemma Pretend a woman watching tv and she is moved by the speaker's credibility and his ability to speak at length on the new product. She also notes that he is attractive.

So in this case she is likely being influenced by 'Peripheral route', but does she also have been influenced by 'central route' ? (Minded because of the credibility of the speaker. Or is that also a characteristic of the peripheral way?)
The terms stem from Petty and Cacioppo's Elaboration Likelihood Model of Persuasion (e.g., 1984, 1986). They posit that persuasion can go via two different routes, depending on whether people have the motivation and the ability to give the persuasive arguments much thought. 

Petty and Cacioppo (1984, p. 70) on the central route:


  One, called the central route, says that attitude change results from a person's careful consideration of information that reflects what that person feels are the true merits of a particular attitudinal position. According to this view, if under scrutiny the message arguments are found to be cogent and compelling, favorable thoughts will be elicited that will result in attitude change in the direction of the advocacy. If the arguments are found to be weak and specious, they will be counterargued and the message will be resisted—or boomerang (change opposite to that intended) may even occur. To the extent that increasing the number of arguments in a message affects persuasion by enhancing issue-relevant cognitive activity, the central route to persuasion has been followed.


Petty and Cacioppo (1984, p. 70) on the peripheral route:


  Attitude changes that occur via the second or peripheral route do not occur because the person has diligently considered the pros and cons of the issue; they occur because the person associates the attitude issue or object with positive or negative cues or makes a simple inference about the merits of the advocated position based on various simple cues in the persuasion context. For example, rather than carefully evaluating the issue-relevant arguments, a person may accept an advocacy simply because it is presented during a pleasant lunch or because the message source is an expert. Similarly, a person may reject an advocacy simply because the position presented appears to be too extreme or because the source is unattractive. These cues (e.g., good food, expert and attractive sources, extreme positions) may shape attitudes or allow a person to decide what attitudinal position to adopt without the need for engaging in any extensive thought about the arguments presented. To the extent that a person agrees with a recommendation because of the simple perception that there are a lot of arguments to support it, the peripheral route to persuasion has been followed.


All attributes given in your example (credibility, attractiveness, eloquence) refer to cues that should be especially relevant if the peripheral route is followed, because they are not arguments about the product itself but refer to the context of the persuasion ("This guy looks legit, sure I'll buy the Slap Chop!").

References

Petty, R. E., &amp; Cacioppo, J. T. (1984). The effects of involvement on responses to argument quantity and quality: Central and peripheral routes to persuasion. Journal of Personality and Social Psychology, 46, 69–81. doi:10.1037/0022-3514.46.1.69

Petty, R. E., &amp; Cacioppo, J. T. (1986). The elaboration likelihood model of persuasion. In L. Berkowitz (Ed.), Advances in Experimental Social Psychology (Vol. 19, pp. 123–205). Academic Press.