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

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.

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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