Question

help! can someone help me with tangent lines. dy=y'dx

Answer 1

i just need help with some practice problems if anybody can help me

Answer 2

Ok, tangent lines. Well, they're straight lines and as such are functions of the form y = mx + b. Thus they have slopes and y intercepts. The nice thing about calculus is that it gives us a way of figuring out what the slope of the line is without too much hassle.
For example what is the tangent line to the function y = x^2 when x = 3.
Here's the magic = if you differential the function and plug in the x value you'll have the slope!!!!! Yay!!

Answer 3

So dy/dx = 2x and when you plug in x = 3, you get that dy/dx = 6. Wow, I just found the slope and I didn't have to use that funky y2-y1/x2-x1 formula when I didn't have any points anyway!

Answer 4

So what's dy/dx for the function y = 2x^3 + 4x when x = 2?

Answer 5

y'=6x^2+4
y'(2)=6(4)+4=28
thus the slope of the tan line is 28 xD

Answer 6

Correctomundo!!