20 POINTS! Using the equation (x^2 − 1)^3, and the interval [−1, 2], find the absolute minimum

-1

Step-by-step explanation:

f(x) = (x² - 1)³

the minimum will occur when the derivative equals zero

f'(x) = 6x(x² - 1)²

0 = 6x(x² - 1)²

if we expand this, we end up with a fifth level polynomial which is VERY difficult to resolve. Let's just take a simple route and know that the 6x = 0 when x = 0 and therefore the whole equation will = 0

x = 0

f(0) = (0² - 1)³ = -1³ = -1

Here's a plot of the equation f(x) = (x² - 1)³ to verify our result.

We see that -1 is the minimum in the range -1 ≤ x ≤ 2

step-by-step explanation:

step 1: solve one of the equations for one of the variables. let's solve the first equation for y:

step 2: substitute that equation into the other equation, and solve for x.

step 3: substitute x = 4 x = 4 x=4 into one of the original equations, and solve for y.