Find out function is increasing and decreasing, Mathematics

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Find out where the following function is increasing & decreasing.

A (t ) = 27t 5 - 45t 4 -130t 3 + 150

Solution

As with the first problem first we need to take the derivative of the function.

A′ (t ) = 135t 4 -180t 3 - 390t 2  = 15t 2 (9t 2 -12t - 26)

Next, we have to determine where the function isn't changing.  It is at,

t = 0

1966_function is increasing.png

Thus, the function is not changing at three values of t.  At last, to find out where the function is increasing or decreasing we have to determine where the derivative is +ve or -ve.

Recall that if the derivative is +ve then the function have to be increasing & if the derivative is -ve then the function have to be decreasing. The given number line gives this information.

2423_function.png

Thus, from this number line we can illustrate which we have the given increasing & decreasing information.

Increasing : - ∞ < t < -1.159, 2.492 < t < ∞

Decreasing : -1.159 < t < 0, 0


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