29th post

Well another week down in calculus lol.. let's go over some easy stuff first:

Tangent lines:

The problem will give you a function and an x value. Sometimes they may give you a y value; if not then you plug the x value into the original function and solve for y to get the y value. Next, you take the derivative of the function and plug in x to get the slope. After that, you plug everything into point-slope form.

First derivative test:

For the first derivative test, you are solving for max and mins and may be trying to see where the graph is increasing and decreasing. You take the derivative of the function and and set it equal to zero and solve for the x values (critical points). Then you set those points up into intervals between negative infinity and infinity. Then, you plug in numbers between those intervals to see if it is positive or negative.

Second derivative test:

For the second derivative test, you are solving to see whether the graph is concave up, concave down, or where there is a point of inflection in the graph. You take the derivative of the function twice and set it equal to zero and solve for the x values. You set those values up into intervals between negative infinity and infinity. You then plug in numbers between those intervals to see if it is positive or negative. If it is positive, it is concave up. If it is negative it is concave down. Where there is a change in concavity, there is a point of inflection.

Some things i do not understand:

The problems where they give you a graph and you have to seperate them into triangles and rectangles to find the area.

Integrals with trig functions in them

Those problems where they give you two equations and you have two variables (most of the time a and b) and you have to solve for one and solve for the other and then set equal.

Hope you all have a great weekend :)