{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

tangent - TANGENT PLANES O Knill Math21a REMINDER TANGENT...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: TANGENT PLANES O. Knill, Math21a REMINDER: TANGENT LINE. Because vectorn = ∇ f ( x , y ) = ( a, b ) is perpendicular to the level curve f ( x, y ) = c through ( x , y ), the equation for the tangent line is ax + by = d , a = f x ( x , y ), b = f y ( x , y ), d = ax + by Example: Find the tangent to the graph of the function g ( x ) = x 2 at the point (2 , 4). Solution: the level curve f ( x, y ) = y − x 2 = 0 is the graph of a function g ( x ) = x 2 and the tangent at a point (2 , g (2)) = (2 , 4) is obtained by computing the gradient ( a, b ) = ∇ f (2 , 4) = (− g ′ (2) , 1 ) = (− 4 , 1 ) and forming − 4 x + y = d , where d = − 4 · 2+1 · 4 = − 4. The answer is − 4 x + y = − 4 which is the line y = 4 x − 4 of slope 4. Graphs of 1D functions are curves in the plane, you have computed tangents in single variable calculus.-3-2-1 1 2 3-6-4-2 2 4 6 8 GRADIENT IN 3D. If f ( x, y, z ) is a function of three variables, then ∇ f ( x, y, z ) = ( f x ( x, y, z ) , f y (...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online