{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# sn8_1 - Math 2433 Week 8 Popper008 15.4 The Gradient as a...

This preview shows pages 1–5. Sign up to view the full content.

Math 2433 – Week 8 Popper008

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
15.4 - The Gradient as a Normal; Tangent Lines and Tangent Planes Suppose that f ( x , y ) is a nonconstant function that is continuously differentiable. That means f is differentiable and its gradient f is continuous. We saw last week that at each point in the domain f (if 0 ) points in the direction of the most rapid increase of f . Also, at each point of the domain, the gradient vector f (if 0 ) is perpendicular to the level curve of f that passes through that point. The vector Is perpendicular to the gradient so it is the tangent vector . The equation of the tangent line is: And the equation of the normal line is:
Example: Write an equation for the tangent line and an equation for the normal line at point P . For f(x,y,z) , the equation for the tangent plane is And the normal line is

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Example: Find an equation for the tangent plane and scalar parametric equations for the normal line at the point P .
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern