2. You can determine where a function increases or decreases by using the derivative to determine the slope at different points. By doing this, you can also determine the location of maximums or minimums if they are in the graph.
3.The chain rule is the process of finding the derivative of a composite function. To apply the chain rule, first take the derivative of the outside and rewrite the interior function. Then multiply the derivative of the inside.
Ex: y = (4-2x)^3 Find the Tangent Line at x=3
3(4-2x)^2 (-2)
-6(4-2x)^2
-6(4-2(3))^2
-6(4-6)^2
=-24
The slope at x=3 is -24.
(4-2(3))^3
(-2)^3
y=-8 when x=3
Plug in to point slope.
y+8=-24(x-3)
y+8=-24(x-3)
y=-24x+64
4. h(x)=f(g(x))
g(-4)=5, g'(-4)=2, f'(g)=20, Solve for h'(x)
g(-4)=5, g'(-4)=2, f'(g)=20, Solve for h'(x)
f'(g(x)) * g'(x)
f'(5) * g(-4) * g'(-4)
20 * 5 * 2
200
On your example of the Chain Rule and finding the tangent line you should show plugging it into the point slope form, all you did was give the slope - intercept form.
ReplyDeleteI like how you included critical point in number 1. I was gone the day we learned this so it helped me out.
ReplyDeleteThanks, T-Money. I fixed it so the people who love my blog wouldn't be confused. You are a true bro.
ReplyDeleteHey R. Fletcher, your explanation of how to use the chain rule is very helpful, especially with the example you gave. WELL DONE!
DeleteAnd no one notices Fletcher's mistake on the last chain rule example. Thank you for putting it on there and there isn't a soul out there that caught it.
ReplyDelete