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24 Cards in this Set
- Front
- Back
If f''(X) is less than zero for an interval, the function is ..... |
Concave for that given interval. Concave means the gradient is decreasing. |
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If f''(X) is greater than zero for an interval, the function is.... |
Convex for that interval. Convex means the gradient is increasing. |
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How do you know where a point of inflection is? |
The point of inflection will be at the point where f''(X) changes sign. (+ To - or vice versa.) |
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Differential of sin(kx)? |
Kcos(kx) |
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Differential of cos(kx)? |
-ksin(kx) |
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Differential of e^kx? |
Ke^kx |
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Differential of ln(X)? |
1/x |
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Product rule for y=f(X)g(X)? |
F(X)g'(X)+g(X)f'(X) |
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Chain rule for y=f(g(X))? |
F'(g(X))*g'(X) |
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Implicit differentiation for the y part. |
Differentiate everything by d/dx, then do one of these three things. |
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How do you prove a number is rational? |
It can be expressed as a/b where a and b are both integers. |
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How would you express 5/(X+1)(X+4) as a partial fraction. |
Firstly split it into a/(X+1) +b/(X+4). Then give them both a common denominator. Set a(X+4) + b(X+1) = 5. Solve by substituting X =-4 and -1. |
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What is the critical factor for a function? |
Each X value must have one y value |
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The inverse of f(X) , f^-1(X), is a reflection of f(X) in what line? |
X=Y |
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What is the formula for the nth term of an arithmetic sequence? |
Un= a+ (n-1)d where a is the first term and d is the difference. |
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What is the formula for the nth term of a geometric sequence? |
Un=ar^n-1. Where a is the first term and r is the common ratio. |
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What is 1+tan²x equal to? |
Sec²x |
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What is 1+cot²x equal to? |
Cosec²x |
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How can you rewrite acos(X) ± bain(X)? |
•Rsin(x±æ) •Rcos(x±ß) Where Rcos(æ)=a and Rsin(æ)=b |
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Where are the routes of a function? |
At the coordinates where f(X) =0 |
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How do you rearrange f(X) =0 so that you can use iteration to find its root? |
Rearrange it into the form X=g(X). From there use the iterative formula Xn+1 = g(Xn) |
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What should you do when integrating something in the form k f'(X)/f(X)? |
Try differentiating ln(X) and then adjust your answer to find the constants. |
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What should you do when trying to integrate k f(X)f'(X)^n ? |
Try f(X)^n+1 and adjust constants. |
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How do you find the angle, o, between the X plane and the vector A? |
Cos(o)=X/|A| |