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

  • Thread starter Thread starter r-soy
  • Start date Start date
  • Tags Tags
    Derivatives
Click For Summary
SUMMARY

The discussion focuses on finding the equation of the tangent line to the curve defined by the function y = x³ - 4x + 1 at the point (2, 1) and determining the range of slopes for this curve. The derivative, y' = 3x² - 4, is essential for solving both parts of the first question. The second question involves differentiating the function y = x - 3√x, applying the power rule, resulting in y' = 1 - (1/3)x^(-2/3). Understanding these derivatives is crucial for analyzing the slopes of tangent lines.

PREREQUISITES
  • Understanding of calculus concepts, specifically derivatives.
  • Familiarity with the power rule for differentiation.
  • Knowledge of polynomial functions and their properties.
  • Ability to evaluate functions and their derivatives at specific points.
NEXT STEPS
  • Study the application of the power rule in more complex functions.
  • Learn how to find the range of slopes for polynomial functions.
  • Explore the concept of tangent lines and their equations in calculus.
  • Practice solving derivative problems involving roots and powers.
USEFUL FOR

Students and educators in calculus, mathematicians interested in polynomial analysis, and anyone looking to deepen their understanding of derivatives and tangent lines.

r-soy
Messages
170
Reaction score
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 .
 
Physics news on Phys.org
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..
 
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.
 

Similar threads

Can you clarify your understanding for parts (a) and (b)?
  • · Replies 11 ·
Replies
11
Views
2K
Can a Function Have Two Different Tangent Lines at the Same Point?
  • · Replies 2 ·
Replies
2
Views
2K
Quadratics Having a Common Tangent
  • · Replies 1 ·
Replies
1
Views
1K
Write the tangent lines to the curve
  • · Replies 1 ·
Replies
1
Views
1K
Find an equation for the horizontal tangent to the curve y=x-3root x
  • · Replies 4 ·
Replies
4
Views
3K
Solving for Tangent Lines: Analytical and Graphical Approaches
  • · Replies 2 ·
Replies
2
Views
1K
Find Values of Osculating Circle Tangent to a Parabola
  • · Replies 4 ·
Replies
4
Views
2K
Lagrange multipliers understanding
  • · Replies 8 ·
Replies
8
Views
2K
Finding the Slope of Secant and Tangent Lines
  • · Replies 2 ·
Replies
2
Views
3K
Calculating the Tangent to a Parametric Curve at a Given Point
  • · Replies 3 ·
Replies
3
Views
2K