Find a normal vector n to the plane z−5(x−2)=2(8−y)

A normal vector is the set of coefficients of x, y, and z when the equation is written in standard (or general) form.

Subtracting the left side, we have

... 2(8 -y) -z +5(x -2) = 0

... 16 -2y -z +5x -10 = 0

... 5x -2y -z +6 = 0 . . . . . general form

A normal vector is (5, -2, -1).

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50