Calculus Homework Help?

First, you take the derivative of the function. Secondly you must find the critical points of the function by setting the derivative equal to zero and solving for x. Once you have your critical points you can make the sign chart and determine the intervals on which each function is increasing or decreasing. You do this by plugging a value above and below each critical point value into the derivative to figure out if the derivative is positive or negative (increasing or decreasing) at each value.

1. Deriv. = 3x^2 + 8x + 4

3x^2 + 8x + 4 = 0

(3x+2)(x+2) = 0

3x = -2 x+2 = 0

x = -2/3 x = -2

the critical points are x = -2/3 and x = -2

now plug in values above and below each critical point to find out if the function is increasing or decreasing on each interval.

so x = -3 makes the deriv. positive.

x = -1 is negative

x = 0 is positive

The function therefore increases from negative infinity to -2, decreases from -2 to -2/3 and increases from -2/3 to infinity.

2. F(x) = 3x + x^-2 - 1

deriv. = 3 - (2x^-3)

2x^-3 = 3

2 = 3x^3

2/3 = x^3

plus/minus the cube root of 2/3 are the critical points.

So plugging in -1, 0, and 1 into the derivative will suit your purposes.