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Ross E.

Third-year computer science student, math tutor for 1 year

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Java Programming

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Question:

What is the purpose of implementing the Comparable interface in Java?

Ross E.

Answer:

The purpose is to be able to compare Objects of the same type to one another which don't have the typical ordering scheme as for example integers (1 < 2 < 3, etc).

Calculus

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Question:

Given: $(f(x)=14x^2+8x$) Find the first and second derivatives of f(x)

Ross E.

Answer:

To find both the first and second derivatives, we must use the power rule: $(\frac{d}{dx}[x^n]=nx^{n-1}$) Thus: $(f'(x)=28x+8$) $(f''(x)=28$)

Algebra

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Question:

Find the x-intercepts of the function: $(f(x)=-3x^2+4x+5$)

Ross E.

Answer:

Finding the x-intercepts means we are finding where: $(f(x)=0$) Setting the given function equal to zero gives us: $(0=-3x^2+4x+5$) Now that we have just one variable, we can solve for x using the quadratic formula: $(\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}$) From the given function we can determine the following: $(\begin{array}{*{20}c} {x = \frac{{ - 4 \pm \sqrt {4^2 - 4(-3)(5)} }}{{2(-3)}}} \\ \end{array}$) $(\begin{array}{*{20}c} {x = \frac{{ - 4 \pm \sqrt {76} }}{{-6}}} \\ \end{array}$) Now it's just arithmetic to determine the two x-intercepts:$(x_1\approx-0.79$) $(x_2\approx2.12$)

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