Blog Post #5

1. f'=0 represents a point in the graph when the slope is zero. This could be a maximum or minimum or a critical point. (Possible maximum or minimum.)

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=-24x+64

4. h(x)=f(g(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