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How do you find out if a function has continuity?
f(x) x=A
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All three of these conditions must be met.
1.) f(A) [is defined]
2.) Lim f(x) when x->A [is defined]
3.) f(A) = lim f(x) when x->A
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A function has graphical continuity if?
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The function is all in one piece
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(Ae^(Bx+C))'=
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(B)(Ae^Bx+C)
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(A(x)B(x))'=
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(A'(x)B(x))+(B'(x)A(x))
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(A(x)/B(x))'=
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(A'(x)B(x))-(B'(x)A(x))/(B(x))^2
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How do you find the slope of a tangent line?
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Take the derivative of the original function and then plug the value of 'x' aka 'x1' into the derivative of the original function to solve for 'm'
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How do you find the equation for the tangent line of a function?
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Find the slope of the tangent line (m)
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Solve for 'y1' by plugging the value of 'x1' into the original function and evaluating
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You now have the value for 'x1', 'y1' and 'm', so now you can plug them into the point slope formula and isolate 'y' to find the equation of the tangent line of the function
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Point Slope Formula
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(y-y1)=m(x-x1)
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((Ax-B)^C)'
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(C(Ax-B)^C-1)*(A)
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How do you find marginal (cost/profit/revenue)?
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Take the derivative of the original function
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Average Rate of Change
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f(x1)-f(x2)/x1-x2
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Instantaneous Rate of Change =
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What is average cost?
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Cost Function / x
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What is marginal average cost?
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Take the derivative of an average cost function
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