Exam (elaborations)
Derivadas y funciones calculo
- Course
- Institution
En este documento encontraremos ejercicios con tematica de derivadas y funciones
[Show more]
Seller
Follow
trujillosamuelchato
Content preview
Guía de actividades y rúbrica de evaluación – Tarea 3 -Derivadas
Anexo 3 - Ejercicios Tarea 3
EJERCICIOS
1. De acuerdo con la definición de derivada de una función, es:
𝒇(𝒙 + 𝒉) − 𝒇(𝒙)
𝒇´(𝒙) = 𝐥𝐢𝐦
𝒉→𝟎 𝒉
Calcular la derivada de las siguientes funciones aplicando la definición
de derivada, es decir, siguiendo el proceso del límite, luego evaluar en
un punto x (escogido por el estudiante) y, finalmente mediante
GeoGebra graficar la recta tangente a la función original y su pendiente
en el punto x escogido, realizar su comprobación y análisis gráfico.
Recuerde que uno de los elementos a evaluar en la actividad es al
análisis gráfico en GeoGebra.
C 𝑓(𝑥) = −2.5𝑥 2 − 4.3𝑥 − 1.2
Solución
𝑓(𝑥 + ℎ) = −2.5 (𝑥 + ℎ)2 − 4.3(𝑥 + ℎ) − 1.2
Simplificamos
𝑓(𝑥 + ℎ) = −2.5 (𝑥 2 + 2𝑥ℎ + ℎ2 ) − 4.3𝑥 − 4.3ℎ − 1.2
𝑓(𝑥 + ℎ) = −2.5𝑥 2 − 5𝑥ℎ − 2.5ℎ2 − 4.3𝑥 − 4.3ℎ − 1.2
Calculamos
𝑓(𝑥 + ℎ) − 𝑓(𝑥) = (−2.5𝑥 2 − 5𝑥ℎ − 2.5ℎ2 − 4.3𝑥 − 4.3ℎ − 1.2) −
(−2.5𝑥 2 − 4.3𝑥 − 1.2)
𝑓(𝑥 + ℎ) − 𝑓(𝑥) = −5𝑥ℎ − 2.5ℎ2 − 4.3ℎ
, Dividimos por h y tomamos el límite de cuando ℎ → 0
−5𝑥ℎ − 2.5ℎ2 − 4.3ℎ
𝒇´(𝒙) = 𝐥𝐢𝐦
𝒉→𝟎 𝒉
𝒇´(𝒙) = 𝐥𝐢𝐦(−5𝑥 − 2.5ℎ − 4.3)
𝒉→𝟎
𝒇´(𝒙) = −5x − 4.3
Evaluamos derivada
𝒇´(𝟐) = −5(2) − 4.3 = −10 − 4.3 = −14.3
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller trujillosamuelchato. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.56. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
52928 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now