Finding Derivatives and Using Point-Slope Form

In summary, The conversation is about finding the derivative of functions and using it to calculate the slope at a given point. The person asking for help is struggling with question 8 and is seeking guidance on how to approach it. The responder suggests using the derivative formula or consulting resources to find the solution. They also mention using the chain rule and point slope form to calculate the slope at a given point.
  • #1
hman24
1
0

Homework Statement



Need help with all of question 8 , any help would be appreciated thanks :D

maths001.jpg



Homework Equations





The Attempt at a Solution


 
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  • #2
so find the derivative of those functions, and plug in x= whatever point they asked about. that's the slope at that point. so for the first one, find f'(x), and then plug in 1.
 
  • #3
hman24 said:

Homework Statement



Need help with all of question 8 , any help would be appreciated thanks :D

maths001.jpg



Homework Equations





The Attempt at a Solution


You DO know that the slope of the tangent line equals the derivative, don't you? Well, in 8(i) you have y = (3x^2 - x - 3)^3. What is preventing you from taking the derivative?

The other are all similar: either use derivative formulas you have covered in class, or look in the book for related material that you may not have covered explicitly, or else consult tables of derivatives, etc. Basically, you just need to start.

RGV
 
  • #4
Do you know how to chain rule?
 
  • #5
Find the derivative (which is the slope), then use point slope form:
y-y1=m(x-x1)
 

1. What is Differential Calculus?

Differential Calculus is a branch of mathematics that deals with the study of rates of change of functions. It helps in finding out the slope or rate of change of a curve at any point.

2. What are the basic concepts of Differential Calculus?

The basic concepts of Differential Calculus include limits, derivatives, and differentiability. Limits are used to define the behavior of a function as it approaches a certain value. Derivatives help in finding the slope of a curve at a given point. Differentiability refers to the smoothness of a function at a certain point.

3. How is Differential Calculus used in real life?

Differential Calculus has various applications in real life, such as in physics, economics, and engineering. It helps in analyzing the change in quantities over time, finding optimal solutions, and predicting future trends.

4. What are the common techniques used in solving Differential Calculus problems?

The common techniques used in solving Differential Calculus problems include the power rule, product rule, quotient rule, chain rule, and implicit differentiation. These rules provide a systematic way of finding derivatives of various functions.

5. How can I improve my understanding of Differential Calculus?

To improve your understanding of Differential Calculus, you can practice solving problems, watch online lectures or tutorials, and seek help from a tutor or teacher. It is also important to have a strong foundation in algebra and trigonometry, as they are essential in solving Differential Calculus problems.

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