Could somebody please give me a hand with this question? Find the line tangent to the curve y=x^2-3x+2 and parallel to the line 4x-2y=7.

Question

Could somebody please give me a hand with this question?  Find the line tangent to the curve y=x^2-3x+2 and parallel to the line 4x-2y=7.

campbell_st · Answer

ok... so can you differentiate 

$$y = x^2 - 3x + 2$$

anonymous · Answer

y=2x-3

campbell_st · Answer

ok... thats a good start. 

next whats the slope of the given line..?

anonymous · Answer

m=2/1

campbell_st · Answer

ok m = 2

so you now need to equate the derivative and the slope of the line to find the x value of the point where the tangent is parallel 

so solve 

2 = 2x - 3

anonymous · Answer

x=5/2?

campbell_st · Answer

ok... now you need to find the point on the curve where the slope is 2

substitute x = 5/2 into your original curve to find the y value for the ordered pair.

anonymous · Answer

Into y=x^2-3x+2?

campbell_st · Answer

thats it ... it will be a fractional answer

anonymous · Answer

Into the derivative of the curve or the original function?

campbell_st · Answer

the original...

anonymous · Answer

*sigh* So simple, yet so difficult.....  Thanks for the help, I really appreciate it.

campbell_st · Answer

lol... yep... one of the keys is realizing that the 1st derivative of an equation gives the equation of the slope of the tangent,. 

so you line is 

y = 2x + b    substitute x = 5/2 and y =       to get your line..

hope it helps