Answer to Question #117915 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

ANSWER : f. $z=5(x-1)$

EXPLANATION

The tangent plane to z=h(x,y) at the point (a,b) is $z-h(a,b)={ h }_{ x }^{ ' }(a,b)\ (x-a)+{ h }_{ y }^{ ' }(a,b)(y-b)$

$a=1,\quad b=5,\ h(a,b)\ =0\quad$

${ h }_{ x }^{ ' }(x,y)=\frac { y }{ x } ,\quad$ ${ h }_{ x }^{ ' }(1,5)=5\quad { h }_{ y }^{ ' }(x,y)=\ln { x } , { h }_{ y }^{ ' }(1,5)=0$ .

So, the tangent plane is $z=5(x-1)$