# Tutor profile: Ross E.

## Questions

### Subject: Java Programming

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

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).

### Subject: Calculus

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

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

### Subject: Algebra

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

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:$(x_1\approx-0.79$) $(x_2\approx2.12$)

## Contact tutor

needs and Ross will reply soon.