Find the (linear) equation of the tangent plane to the surface z=5y2−3x2+x at the point (2,−1,−5). your answer should be in the form of an equation, e. g., something like ++cz= or −x0)+−y0)+c(z−z0)=0 would work.

The equation of the tangent plane to the surface is given by

Step-by-step explanation:

We can find the normal of the surface using the gradient over f(x,y,z), where the function is

And the gradient is

Then the normal at the point (2,-1, -5) is

Then the equation of the tangent plane to the surface is given by

Replacing the given point and the normal we get

We can simplify a bit to get into standard form