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### 17 Cards in this Set

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 find the zeros set function = 0, factor or use quadratic equation if quadratic, graph to find zeros on calculator find equation of the line tangent to f(x) on [a,b] take derivative: f'(a) = m use y - y1 = m(x - x1) find equation of the line normal to f(x) on [a,b] same as above but take the negative reciprocal of the derivative at a (f'(a)) show that f(x) is even show that f(-x) = f(x) symmetric to y-axis show that f(x) is odd show that f(x) = -f(x) symmetric to origin find the interval where f(x) is increasing find f'(x), set both numerator and denominator to zero to find critical points, make sign chart of f'(x) and determine where it is positive find interval where the slope of f(x) is increasing find the derivative of f'(x) = f"(x), set both numerator and denominator to zero to find critical points, make sign chart of f"(x), and determine where it is positive find the minimum value of a function make a sign chart of f'(x), find all relative minimums and plug those values back into f(x) and choose the smallest find the minimum slope of a function make a sign chart of the derivative of f'(x) = f"(x), find all relative minimums and plug those values back into f'(x) and choose the smallest find critical values express f'(x) as a fraction and set both numerator and denominator equal to zero find inflection points express f"(x) as a fraction and set both numerator and denominator equal to zero; make sign chart of f"(x) to find where f"(x) changes sign (+ to – or – to +) show that lim as x approaches a of f(x) exists show that the lim f(x) is the same from the left and right lim as x approaches a- of f(x) = lim as x approaches a+ of f(x) show that f(x) is continuous show the following: 1) that lim as x approaches a of f(x) exists 2) that f(a) exists 3) that the lim as x approaches a of f(x) = f(a) i.e. if you're given a function x^2+x+3, and you want to find the lim as x approaches 4 (just some a), then you plug in 4 in the function find vertical asymptotes of f(x) do all factor/cancel of f(x) and set denominator = 0 find horizontal asymptotes of f(x) find lim as x approaches infinity- of f(x) and lim as x approaches infinity+ of f(x) find the average rate of change of f(x) on [a,b] find (f(b) - f(a))/(b-a) find instantaneous rate of change of f(x) on a find f'(a)