Answer to Question #118267 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

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