Calc

 for this unit in calculus we evaluated a function I choose F(x)=x(x+4)*0.5*-3/x^2 or f(x)=-1.5+-6x^-1 which shows the ratio between the squares of numbers and the triangle numbers with the derivative being F'(x)=6x^-2 the if the normal function is speed the derivative is acceleration to evaluated it on paper the I chose F(4) and the F(4)=-1.5+-6x^-1=-1.5+-6*.25=-1.5+-1.5=3 using the graph I evaluated f(-4)

i made an estimate of the slope at f(-3)

f(-3.1)-f(2.9)/3.1-2.9=

-1.5+-6*3.1^-1 +1.5+-6*2.9^-1/3.1-2.9=

-6*(3.1^-1)-6*(2.9^-1)/.2

-6*.32 -6*.34/.2

-1.92-2.04/.2

3.96/.2 = 19.8 but the f'(-3) = .66667

for the point (-3,f(-3)) instantaneous slope is y - 0.5 = 2/3(x + 3)

the (d/dx)^2f(x)=-12x^-3

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