A differentiable function f(x, y) has the property that f(5, 1) = 4 and ƒâ(5, 1) = −7 and f(5, 1) = 4. Find the equation of the tangent plane at the point on the surface z = f(x, y) where x = 5, y = 1. z =

The parametric curve x= 4t4 + 4t 2 + 1, y= 5t3 – 5t has two tangent lines at the point (9, 0). Find their slopes.

F(x, y) = (2x + y3, 3y - x4} across the unit circle

answer all the questions and show all work!

Determine the coefficients a, b, c and d so that the curve y = ax* + bx³ + cx² + dx + e will pass through the points (0, 3), (–2,7) and have an inflection point at (1,4) with horizontal tangent.

I'm stuck on this one. I need help please & thank you!!

An object is traveling along the line y = 2x + 1 heading up and to the right. If the temperature at (x, y) in degrees celsius is given by f(x, y) x²y + x − y, and if the plane is measured in meters, what is the instantaneous temperature change the object is experiencing at the instant when x 3? - =

A curve in the xy-plane is defined by xy2-x3y-=6a) Find dy/dxb) Find an equation for the tangent line at each point on the curve with x-coordinate 1. c) Find the x-coordinate of each point on the curve where the tangent line is vertical.