Wong oral quiz (table)

How to estimate the derivative of a point in a table?

You use MVT for the derivative, the function must be differentiable, using the points on both sides if the point is on the table or by using the two points whose interval includes the point we need.

How to find the unit of a derivative?

You put y’ = dy/dx where it is equal to the unit of y over the unit of x.

How many ways can you find integral?

You use Riemann sum approximation (LRAM, RRAM, MRAM) or trapezoidal sum approximation.

How to do LRAM, RRAM, MRAM?

LRAM is draw left corners, RRAM is draw right corners, MRAM is draw umbrellas.

Whats the formula to find trapeziodal sum?

½ x difference of h x ( base2 +base 1)

shortcut when all hs difference is the same is ½ (h)(b1 + (any base in between x 2) +bn)

How to tell if LRAM, RRAM over or underestimate?

Draw the graph, decreasing or increasing, and from there draw the corner to see if it under or overestimate.

How to tell if MRAM over or underestimate?

For MRAM use concavity and tangent line to check, where if it concave up means it is under, and if it is concave down it is over.

How to find the unit of an integral?

It is the intergral of f(x) dx from a to b is equal to the unit of f(x) multiplied by the unit of x.

How to find the meaning of a derivative?

You need to have 3 things on the left side + right,(ex. f’(x)=?) f is given in the problem, where the rate of f at time t is decreasing/increasing at a rate of ? unit.

How to find the meaning of a integral?

Multiply the unit of f(x) with unit of x, Integral of f’(x) dx from a to b is the change (amount) of f over [a,b].

How to find the average for f(x)?

Use MVT for intergral, reg f(x) [a,b]/b-a

How to find the average rate for f(x)?

If f(x) is given but the rate is not given use, (integral f’(x) dx from a to b)/(b-a) = (f(b)-f(a))/(b-a),(must use f’), if the rate is already given use integral f(x) dx from a to b)/(b-a) (do not use f’, if the unit of f contains per = rate of f).

How to find t when given W or W’

W is a dummy variable, W use IVT, and for W’ use MVT

How to tell if the rate is increasing at an increasing rate?

Increasing rate means y’’ is greater than 0, decreasing rate means y’’ is less than 0.

How to find x so y is increasing/decreasing most rapidly?

Find the abs max of y’ and abs min for decreasing.

How to find rel(local) max(min)?

You can find this by first Derivative Test or 2nd derivative test(2 conditions for 2nd der, differentiable, y’=0).

How to find absolute maximum(minimum)?

You can do this by Candidate test or first Derivative Test with endpoints(when found the max,min, plug into y function to see if its abs). if the interval it is abs(global)

How to approximate y?

There is 1 way to approximate y, by using tangent line approximation.

How to find whether the tangent line over or under approximates?

Where if it concave up means it is under, and if it is concave down it is over.

What do u need for tangent line approximation?

You need 1st point (x,y) and 2nd point (x,y) and then slope.

What is another name for local and global?

Relative and Absolute