with the derivative of P(X) = -4x^3 + 64x - 100......do i need to solve for X to find where p(x) is decreasing

Question

decreasing and increasing.........
how do i do that? steps?

OK SORRY. the px above IS the derivative im working w/

Answer 1

The derivative is P´(x) = -12x^2 + 64

The function is decreasing when the derivative is negative.

You must study the signal of the function P´(x)

a) find the roots: -12x^2+64 = 0 => x^2 = 64/12 = 16/3
and the roots are: x1= 4/sqrt(3) and x2= -4/sqrt(3)

b) the signal of P´(x) is negative for x in the interval

(-4/sqrt(3) , 4/sqrt(3) ) and the function P(x) is decreasing

c) the signal of P`(x) is positive for x < -4/sqrt(3)
or x> 4/sqrt(3) and the function is increasing

Answer 2

The first derivative tells you when a function is increasing or decreasing. For
P(X) = - 4x^3 + 64x - 100
P'(X) = - 12x^2 + 64
The derivative has two 0's,
x = ± (4/3)√3, or x ≈ ± 2.309401
The slope is
negative for x < - (4/3)√3,
positive for - (4/3)√3 < x < (4/3)√3, and
negative for x > (4/3)√3

Answer 3

1. Find the derivative of the function.
2. Set it equal to zero and solve for x.
3. Test x-values to the left and right of your answers for (2) to find out if the derivative is positive or negative at those points.
4. If a derivative is positive, the function is increasing. If the derivative is negative, it is decreasing. The numbers you found in (2) are maximums, minimums, or points of inflection.

Answer 4

find the derivative of the function

-12x²+64
now you find the zeros of this equation which would be
±√64/12 -->±√16/3

then that would be a negative parabola, so you know between
-√16/3 & +√16/3 the rate of change will be increasing, so P(x) won't be increasing in that range.

so p(x) is decreasing when x≤-√16/3 and when x≥√16/3.

Answer 5

First take the derivative of P(X) getting

dP/dx = -12x^2 + 64

Now solve for x and each value of x will be either a maximum or minimum point of that function.

Now test points on either side of the Max and Min points and see if hte value is higher or lower to determine if it is increasing or decreasing and thus you will be able to tell the intervals on which it does increase or decrease

Answer 6

Yes, but since the derivative of p(x) will just be a parabola it should be a pretty basic thing to do.