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y=(6x^9 +x^8)/(2x^4), work out the value of d^2y/dx^2 when x=0.5

The question can be represented by the notation d 2 y/dx 2 |x=0.5 , meaning the second derivative of y with respect to x resolved at x=0.5. Since y is in the form f(x)/g(x), the quotient rule could be used, ...
OC
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y = (x+4)(6x-7). By differentiating, find the x coordinate of the maximum of this equation.

y=(x+4)(6x-7)y=6x 2 +17x-28dy\dx = 12x + 17To find the x coordinate of the stationary points of y, let dy\dx=012x+17=0x=-17\12
AS
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Express f(x) = ln(x+1) as an infinite series in ascending powers of x up to the 3rd power of x

Recall that the Maclaurin series for f(x) is f(x) = f(0) + f'(0)x + f''(0)x 2 /2! + ... + f (r) (0)x r /r! + ... Here f(0) = ln(1+0) = ln1 = 0 , f'(x) = 1/(1+x) using the chain rule. f'(0) = 1/1 = 1 , f''(x)...
CP
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Why does the discriminant b^2-4ac determine the number of roots of the quadratic equation ax^2+bx+c=0?

The rule for the discriminant: if b^2-4ac>0 then the quadratic has two roots if b^2-4ac=0 then the quadratic has one root if b^2-4ac<0 then the quadratic has no rootsRecall that the formula for solving...
DG
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Find dy/dx when y=2x^(4)+3x^(-1)

To differentiate this equation we use the power rule. This means that we times the power by the coefficient, this now becomes our new coefficient. Then you subtract 1 from the old power and this becomes your...
RC
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