Question

At what point on the graph y=1/2x^2 is the tangent line parallel to the line?

Answer 1

what line is the question referring to?

Answer 2

sorry, i missed that. It's 2x-4y=3

Answer 3

ok...
so all we need is the slope of the line 2x - 4y = 3 so we can set the slope of the tangent line equal to that. did you find the derivative of y = 1/2x^2 ?

Answer 4

x?

Answer 5

is that the derivative?

Answer 6

Yes it is

Answer 7

ok....
since the derivative gives the slope of the tangent line at any point, then all we need to do now is set that to the slope of the line 2x - 4y = 3.

what's the slope of 2x - 4y = 3 ????

Answer 8

y=1/2x - 3/4

Answer 9

just the slope.... what is it?

Answer 10

1/2

Answer 11

ok... good... lemme summarize....

Answer 12

dy/dx = x
slope = 1/2

so if we set dy/dx = slope, we have:
x = 1/2

this is the x-coordinate of the point on the graph where the tangent line is parallel to
2x - 4y = 3. do you know how to get the y-coordinate?

Answer 13

Is that where we look for the x value?

Answer 14

no... we already have the x value. we only need the y value (coordinate) of the point on the graph.

Answer 15

hint: how do you plot points on the graph of y = 1/2x^2 ? how do you calculate the y-value when x=1/2 ?

Answer 16

need another hint?