Answer to Question #118082 in Calculus for Olivia

Question

The equation of the tangent plane to h(x,y)=yln(x) at the point (1,5) is
Select one:
a. z=1/5x+1/5y

b. z=x+y


c. z=1/4x+1/4y


d. z=4(x−1)


e. z=5(x+1)


f. z=5(x−1)

Answer 1

$Since \ h(x,y)=yln(x), we \ get \\ h_x(x,y)=\frac{y}{x} \ and \\ h_y(x,y)=\ln(x).\\ at (1,5) , we \ obtain\\ h_x(1,5)= 5\ and \\ h_y(1,5)=\ln(1)=0.\\ As \ at (1,5) \text{the equation of }\\ \text{the tangent plane to }h(x,y) is \\ z=h_x (1,5)(x-1)+h_y(1,5)(y-5)\\ So, we \ get \\ z=5(x-1).\\ \text{This implies that the correct answer is }\\ f.$