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The question can be represented by the notation d²y/dx²_|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), th...

y=(x+4)(6x-7)y=6x²+17x-28dy\dx = 12x + 17To find the x coordinate of the stationary points of y, let dy\dx=012x+17=0x=-17\12

Recall that the Maclaurin series for f(x) is f(x) = f(0) + f'(0)x + f''(0)x²/2! + ... + f^(r)(0)x<...

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 ...

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 y...