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19 Cards in this Set
- Front
- Back
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Definition of a limit
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f function defined on an open interval containing a
f'(a)= lim h->0 [f(a+h)- f(a)]/h |
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Applications of derivative (2)
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1)derivative is the m of tan line
2)velocity- the derivative (with respect to time) of a postion function |
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Derivatives on a closed interval
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f is differentiable on a closed interval [a,b] if it is differentiable on an open interval (a,b) and if the right hand and left hand limits exist and match
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finding derivatives: constant rule
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f'(c)=0
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finding derivatives: derivative of x with respect to x
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1
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finding derivatives: power rule
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take the power down and take the power down
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finding derivatives: constant times function
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constant times derivative of the function
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finding derivatives: addition and subtraction
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derivative of the sum or difference is the sum or differences of the derivatives
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finding derivatives: product rule
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first times derivative of the second plus second times the derivative of the first
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finding derivatives: quotient rules
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low d high MINUS high d low over low low
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speed
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absolute value of v(t)
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acceleration
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s''(t)
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chain rule
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for composite functions, work outside in
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implicit differentiation
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differentiate both sides, whenever a y part is differentiated multiply by y'
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higher order of derivatives
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if the derivative of a function is a function, it can be differentiated the indicated number of times
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Related rates: steps to solve
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1) draw picture
2)label everything 3) find relationship between quantities 4)differientiate with respect to time to find the relationship between rates 5)plug in known values and solve for unknown |
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Area:
rectangle square circle triangle |
lw
s^2 pi r^2 (1/2)bh |
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Volume:
prizm pointed things cube sphere |
Bl
1/3 Bl s^3 4/3 pi r^3 |
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Newton's Method
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x sub n+1= x sub n minus f(x subn)/ f'(xsubn)
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