MATH
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# Increasing magnitude means slope that means that f is

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Increasing magnitude means + slope < that means that f’’ is + < concave down C.D <it's about magnitude increasing or decreasing SN> ALWAYS FACTOR IF YOU CAN Take the double derivative and find the inflection points < this is where the graph changes from cu to cd Make a sign chart of inflection points and see if + (cu)to the right and left or (cd). 2nd driv test If f’(x)=0 and f’’(x) >0 it is a local max If f’(x)=0 and f’’(x) <0 it is a local min 11.1 inclass - Roc problems - if there is a variable that we don't know or don't care about we need to make

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sure that everything is as it should be 4.1 Functions have to be turned into something that can be solved for 0 < factors, rationals For rationals solve top and bottom for 0 <if a a b = 0 thenamust = 0 First driv rule if a function is continuous on an interval Then there is a global max and min (still might be there if conditions are met) Critical values > were derivative equals zero , or is undefined , or at the endpoints Use critical values to test for y’s of the functions at those points 4.3 We can see if the critical values mark local maxs and min by texting the values next to the for their derivatives The directing tells us what is happening beside the points - Positive f’ - increasing - Negtive f’ - decreasing ! To do this we do a sign test - mark intervals on a number line and test values in between 3.10 - We are working at one monument to get a a long term answer We use the tangent line to find other values that are locally linear 1) Find the tangent line at a point “close” to the target line 2) Evaluate at the target Models are more practical than tests Testing model accuracy - F(x) -l(x) < we want to know the absolute value Differentials < study of small differences. If dy/dx = f’(x)
Then dy = f’(x) * dx (only good for small difference because that is how derivative is defined) 4.0- Maximum > the highest y for a value of x Local - in a defined range larger than the values on either side Global - Over all highest y (not infinity if not a global)< sometimes a global is not a local max if it is not larger on both sides For extremes f’(c) = 0 Some time there will be an extreme and f’(c) != 0 due to a corner Some functions have f’(c) = 0 because of a straight part of the function but no extreme 10.30- Rate of change At step 5, simplify if you can Only include constants in step 5 Make sure you pay attention to the decreasing roc. Saying that it is decreasing means it doesn't need a negative. 10.8 Implicit derivative - we define the the derivative in terms of a value such as X. So when taking the Derivatives of a part of a function he take it as the change in the output as X changes. So d dx . When it come to values that include a Y we have to take the result of that function of the change in the Y value. So d dy but that is not consistent with our definition of a derivative so it must be multiplied by dy dx which reconciles this <this is the chain rule.

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