Solving for Tangent Lines and Range of Slopes for a Given Curve

In summary: For problem 2, use the power rule to find the derivative. In summary, the conversation is discussing two questions related to finding the equation for tangent to a curve and the range of values for the curve's slope, and finding the derivative of a function using the power rule. The speaker is asking for help in solving these problems.
  • #1
r-soy
172
1
Hi all





I hve two Q I want the explaine how to solve



Q1 :(A) Find an equation for tangent to curve y = X^3 - 4X + 1 at the point (2,1)



(b ) What is the range of values of the curve's slope





Number ( A ) I can solve it but ( B) I face problem to solve







Q 2 derivative y = x - 3root X



please I want the explaine how to solve How to solve each one .
 
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  • #2
Use the power rule for Q2. y = x - x^(1/3)
y' = 1 - x^(-2/3)/3
Power rule is d/dx x^n = nx^(n-1), which I'm sure you know..
 
  • #3
r-soy said:
Hi all

I hve two Q I want the explaine how to solve
Q1 :(A) Find an equation for tangent to curve y = X^3 - 4X + 1 at the point (2,1)
(b ) What is the range of values of the curve's slope

Number ( A ) I can solve it but ( B) I face problem to solve

Q 2 derivative y = x - 3root X

please I want the explaine how to solve How to solve each one .
In problem 1, what did you get for y'? You need that function so that you can find the range of values of the slopes of the tangent lines for the curve.
 

Related to Solving for Tangent Lines and Range of Slopes for a Given Curve

1. What are derivatives and why are they important in science?

Derivatives are mathematical tools used to measure the rate of change of a variable with respect to another variable. They are important in science because they allow us to analyze and understand the behavior of complex systems and phenomena, such as changes in temperature, speed, or concentration over time.

2. How do you calculate derivatives?

There are several methods for calculating derivatives, but the most common is using the concept of limits. By taking the limit of a function as the change in the independent variable approaches zero, we can find the derivative at a specific point.

3. What are the different types of derivatives?

The most commonly used types of derivatives are the first derivative, also known as the slope or rate of change, and the second derivative, which measures the rate of change of the slope. There are also higher-order derivatives, which measure the rate of change of the second derivative, and so on.

4. How are derivatives used in real-world applications?

Derivatives have many practical applications in fields such as physics, economics, and engineering. For example, they can be used to model and predict the motion of objects, determine optimal solutions in financial markets, and design efficient systems.

5. What are the limitations of using derivatives?

While derivatives are powerful tools, they have some limitations. They can only be applied to continuous and differentiable functions, and they may not accurately represent nonlinear or discontinuous systems. Additionally, the process of taking derivatives can be time-consuming and complex for more complicated functions.

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