Re: Help with Derivatives.

I have figured out (c) and (d) for you. Maybe someone else that knows more can help you with (e) and (f).

f' = (4x^3 - 36x)/5

To figure out where its decreasing or increasing, we need to find the critical point. Which is found by setting the first dervative equal to 0, and then solving for x.

0 = (4x^3 - 36x)/5

0 = x(4x^2 - 36)

0 = x(2x+6)(2x-6)

So x = 0, x = -3, x = 3 are our options.

To classify them as a critical point we need to test points within our critical points, and observe the behavior when we plug them into f'(x)... observing meaning just check whether they are + or -

f'(-4) = -

f'(-1) = +

f'(1) = -

f'(4) = +

So we are decreasing from x = -∞ to x= -3

Then increasing from x = -3 to x = 0

Then decreasing from x= 0 to x = 3

Then increasing from x = 3 to x = ∞

So our interval of decreasing:

(-∞, -3] U [0, 3]

And our interval of increasing:

[-3, 0] U [3, ∞)

Re: Help with Derivatives.

The function f is increasing if $\displaystyle f'(x)>0$, decreasing if $\displaystyle f'(x)<0$, concave upward if $\displaystyle f''(x)>0$, and concave downward if $\displaystyle f''(x)<0$. Since you've calculated the first and second derivatives already, it's only a matter of determining where they're positive and negative.

- Hollywood

Re: Help with Derivatives.

Let f(t) = 9t^4 - 7t^2 + 12t -4 , Find (laplace) ** L**[d^2f/dt^2]

I get answer 108(2/s^3) - 14/s

Is it my answer correct?