How do you find the equation of a tangent line? how does it differ from a regular derivative. Give an example of finding an equation of a tangent line and an example of finding a regular derivative. Include the directions that would be given with each problem.
The difference of find a tangent line and just a derivative is when your solving to find a tangent line once you get your derivative you have to keep going till its in point slope form. When you’re trying to find the equation of a tangent line you start by taking the derivative. once you have your derivative you plug in the x-value. If you’re not given a y-value, plug x-value into the original equation to get your y-value. Then plug the values you got for y, x, and slope into point slope form. Here an example:
ReplyDeleteFind an equation of the tangent line of f(x)=x² when x= -2
F(x)=2x
M=2(-2)
X= -4
(-2,4)
Y= (-2)²
Y= 4
y- 4= -4(x+2)
to find a derivative you use the power and constant rules. The constant rule states that the derivative of any constant is 0. the power rule states that whatever the exponent is on a variable you pull it to the front and the exponent subtracted by one. nx^n-1
f(x)= x^3
f(x)= 3x²
To find an equation of a tangent line, you must take the derivative of the function and plug in the x-value. (If not given a y-value, plug into the original equation to get the y-value.) Then plug the values into point slope which is: y - y1 = m(x - x1)
ReplyDeleteExample: Find an equation of the tangent line to the graph of f at the given point
f(x) = x/x+4, (-5, 5)
= (x+4)(1) -[(x)(1)] / (x+4)^2
= x+4-x / (x+4)^2
= 4/(x+4)^2
m = 4/(-5+4)^2 = 4/1^2 = 4
point slope: y - 5 = 4(x + 5)
To find a regular derivative you can use the whole limit process or the shortcut.
Example:
use shortcut
f(x) = x^2
= 2x
When finding the equation of a tangent line, you first have to find the derivative. unlike finding you when you would stop at that there are more steps to find a tangent line.
ReplyDeleteafter you have the derivative, you then move forward to plug in the x value from the
point given and find the slope of the tangent line.
after doing so you plug in the point slope formula getting your final answer.
Example of finding a derivative:
3x^2
here using the shortcut would be best.
3(2x)
this answer would be 6x.
if you wanted to find the tangent line
from here you would do so:
the point is (-2,1)
6(-2)
=-12
y-1=-12(X+2)
this is the equation of the tangent line.
To find the equation of a tangent line you first take the derivative and plug in the x-value. If you are not given a y-value, plug into the original equation to get the y-value. Then plug these values into the point slope formula. The difference between this and a regular derivative is that when you take a regular derivative you only take the derivative and don't plug in anything.
ReplyDeleteFind an equation of the tangent line to the graph of the function f(x)=x^2+6x+3 at the point (-4,-5).
Derivative= 2x+6
Plug in -4 for x and you get -2
then plug into point slope form and you get y+5=-2(x+4)
y=-2x-8
Finding the derivative:
Find the derivative of the function:
x^4+3x
Use the shortcut-take exponent and move to front of (x), then subtract the exponent by one.
4x^3+3
To find an equation of a tangent line, you must take the derivative of the function and plug in the x-value. If you are not given a y-value, plug into the original equation to get the y-value. Then plug these values into the point slope formula. The point slope which is: y - y1 = m(x - x1.
ReplyDeleteTo find a regular derivative you can use the whole limit process or the shortcut.