Final Review
Quiz yourself by thinking what should be in
each of the black spaces below before clicking
on it to display the answer.
Help!
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Define a tangent line | The tangent line to the curve y = f(x) at the point P(c, f(c)) is that line through P with slope m= lim (as h approaches 0) (f(c+h)- f(c))/h proivided the limit exists and is not infiniety or negative infinity.
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Define derivative | The derivative of a function f is another function f’ whose value at any number x is f'(x) = lim(as h approaches 0) [f(x+h)- f(x)]/h
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Thm. differenciability implies what? | continuity; If f’(c) exist, the f is continuous at c
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Thm: Constant Function Rule | If f(x) = k, where k is a constant, then for any x, f’(x) = 0
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Thm: Identity Function Rule | If f(x) = x then f’(x) = 1
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Thm: Power Rule | If f(x) = x^n, where n is a positive integer, the f’(x) = nx^n-1; that is Dx(x^n) = nx^n-1
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Thm: Constant Multiple Rule | If k is a constant and f is a differentiable function, then (kf)’(x) = k * f’(x)
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Thm: Sum Rule | If f and g are differentiable functions, then (f+g)’(x) = f’(x) + g’(x)
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Thm: Difference Rule | If f and g are differentiable functions, then (f-g)’(x) = f’(x) - g’(x)
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Thm: Product Rule | If f and g are differentiable functions, then (f*g)’(x) = f(x)g’(x) + g(x)f’(x)
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Thm: Quotient Rule | Let f and g be differentiable functions with g(x) does not equal zero. Then (f/g)'(x) = [g(x)f'(x)-g'(x)f(x)]/(g(x))^2
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Derivative of sin x | cos x
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Derivative of cos x | -sin x
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Derivative of tan x | (sec x)^2
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Derivative of cot x | -(csc x)^2
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Derivative of sec x | sec x tan x
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Derivative of csc x | -csc x cot x
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Thm. Chain Rule | Let y = f(u) and u = g(x). If g is differentiable at x and f is differentiable at u = g(x), then the composite function f(g(x)) is differentiable at x and f(g(x))' = f'(g(x))g'(x)
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Review the information in the table. When you are ready to quiz yourself you can hide individual columns or the entire table. Then you can click on the empty cells to reveal the answer. Try to recall what will be displayed before clicking the empty cell.
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You may also shuffle the rows of the table by clicking on the "Shuffle" button.
Or sort by any of the columns using the down arrow next to any column heading.
If you know all the data on any row, you can temporarily remove it by tapping the trash can to the right of the row.
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Created by:
agea
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