Question
Find an cquation of the tangent plane to the givensurface at the specified point.$$z=3(x-1)^{2}+2(y+3)^{2}+7, \quad(2,-2,12)$$
Step 1
The partial derivative with respect to x is given by: $$ \frac{\partial z}{\partial x} = 6(x-1) $$ and the partial derivative with respect to y is given by: $$ \frac{\partial z}{\partial y} = 4(y+3) $$ Show more…
Show all steps
Your feedback will help us improve your experience
Caelan Thomas and 92 other Calculus 3 educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find an cquation of the tangent plane to the given surface at the specified point. $$ z=3 y^{2}-2 x^{2}+x, \quad(2,-1,-3) $$
PARTIAL DERIVATIVES
Tangent Planes and Linear Approximations
Find an equation of the tangent plane to the given surface at the specified point. $z=3(x-1)^{2}+2(y+3)^{2}+7, \quad(2,-2,12)$
Multivariable Calculus
Find the equation of the tangent plane to $z=x^{2}+2 y^{3}$ at (1,1,3)
Differentiation
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD