equation of a tangent

[Guest]

A tangent to the parabola y=3x^2-7x+5 is perpendicular to x+5y-10=0. Determine the equation of the tangent. I know the slopes have to be the same, but that's all I know. How do you figure this out?thanks

 

[stapel]

I know the slopes have to be the same....

The slopes of what have to be the same as which?

What is the slope of "x + 5y - 10 = 0"? (You learned this back in algebra.)

What then is the perpendicular slope? (This was also covered in algebra.)

So what slope are you looking for?

Since "derivative" is "slope at a point", take the derivative, set it equal to the desired slope, and solve for x.

If you get stuck, please reply showing how far you have gotten in following these instructions. Thank you.

Eliz.

 

[Guest]

oh I think I was thinking of the word "parallel" , anyways, x+5y-10=0, the slope would be -1/5? then the other equations slope should be 5? I don't get what to do next..

 

[stapel]

[T]he slope [of x + 5y - 10 = 0] would be -1/5?

Yes.

[T]hen the other [line's] slope should be 5?

Yes

I don't get what to do next.

Take the derivative, set it equal to the desired slope, and solve for x.

Eliz.

 

[Guest]

3x^2-7x+5, f'(x)=6x-7
6x-7=5
x=12/6
x=2

but what do you do with the x? y=mx+b
y= 5(2)+b? how do you get the y to find b then?

 

[stapel]

You are given that y = 3x² - 7x + 5, and you have determined that x = 2. So plug "2" in for "x" to find the corresponding value of "y".

You also know the slope, so you have "m". So plug x, y, and m into "y = mx + b", and solve for "b".

Then write out your tangent-line equation.

Eliz.

 

[Guest]

thanks!