Purchase Solution

Equation of tangent line to a curve

Not what you're looking for?

Ask Custom Question

Find the equation of the tangent line to the graph of the function f(x) = x + (4/x) at the point (4, 5).

Purchase this Solution
Solution Summary

The equation of the tangent line to the graph of the given function at the given point is provided, along with a detailed explanation of how it can be determined.

Solution Preview

We will find the point-slope form of the equation of the tangent line to the graph of the function f(x) = x + (4/x) at the indicated point.

The point-slope form of a line is y - y_0 = m*(x - x_0), where (x_0, y_0) are the coordinates of a specific point on the line and m is the slope of the line.

The indicated ...

Solution provided by:
Georgia Martin, PhD
Education
  • AB, Hood College
  • PhD, The Catholic University of America
  • PhD, The University of Maryland at College Park
Recent Feedback
  • "Thanks for your assistance. "
  • "Thank you. I understand now."
  • "Super - Thank You"
  • "Very clear. I appreciate your help. Thank you."
  • "Great. thank you so much!"
Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

View More Free Quizzes
Related BrainMass Solutions

  • Finding the tangent to a curve. Picture included.

    5407 Finding the tangent to a curve. Picture included. Find an equation of the tangent line to the curve Y= x3 - 3x2 + 5x that has the least slope.

  • Equation of the Line Tangent to the Curve

    135905 Equation of the Line Tangent to the Curve Hi, this was your response since dy/dx means the slope of a tangent to the curve at a certain point there fore dy/dx= (3 x^2)- (6*2*x^1) dy/dx = (3x^2) - (12x) Equation of the line tangent

  • Find an equation of a tangent line.

    135901 Findong an equation of a tangent line.

  • Equations of Tangent lines and Intercepts in Terms of a Variable

    intercept of the tangent line at x = -1 (c) find the x intercept of the tangent line at x=-1 Let f(x) = a(7-x^2) where a is not equal 0 (a) find, in terms of a, the equation of the line tangent to the curve at x = -1 (use pt slope) Solution

  • Parametric Curves

    For the parametric curve given by: x = e^(sqrt(t)) , y = t - ln(t^2) (a) find an equation of the tangent line to this curve at the point corresponding to t=1. (b) For what values of f is the tangent line vertical?

  • Equation of a straight line which is tangent to a curve

    5295 Equation of a straight line which is tangent to a curve For the curve f(x) = x - 1/3x^2 (one third x squared), find the equation of the straight line which is tangent to this curve at the point x = 1. See attachment for diagram.

  • Find parametric equations for the tangent line at the point

    on curve , we find the value of parameter t, By substituting to , the direction vector of the tangent line can be found as Therefore, the parametric equation of the tangent line, r(t), at point on the curve can be found as or ,

  • Tangent Line to a Curve

    5394 Tangent Line to a Curve Find an equation of the tangent line to the curve, Y = x^3 - 3x^2 + 5x that has the least slope. Make sure to show all of the required steps. Let's assume that the curve goes through a point (x0,y0).

  • Finding the tangent and normal to a curve

    a) When x = 2, y = 8 - 2*4 - 2 + 9 = 7 Since coordinates of P satisfy the equation of the curve, it lies on this curve. b) dy/dx = 3 x^2 - 4 x - 1 at P, dy/dx = 3* 4 - 4* 2 - 1 = 12 - 8 - 1 = 3 Slope of the tangent line at P is 3.

  • Astroids and Tangent Lines

    45426 Asteroids and Tangent Lines The graph of x^(2/3) + y^(2/3) = 1 is an astroid. How can I find the equation of the tangent line at (1/8, 3√3 /8). Are there any points on the curve at which no tangent line can be defined?

View More Related Solutions