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I got absolute minimum wrong

9514 1404 393

Step-by-step explanation:

The absolute extremes will be at one of two locations:

Here, the absolute maximum occurs where the derivative is zero (and the second derivative is negative).

  f'(x) = 3x^2·e^-x -x^3·e^-x = x^2·e^-x·(3 -x)   ⇒   f'(3) = 0

The absolute minimum occurs at the left end of the interval, where both x^3 and e^-x have large magnitude.

The minimum is ...

  (-4)^3×e^-(-4) ≈ -3494.21 . . . . six significant figures

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A graph can show you the function tends toward -∞ as x goes to large negative values. Hence, the absolute minimum on an interval beginning in the left half-plane will be at the left end of the interval.

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: no, but if it does it's a obvious pattern.

step-by-step explanation: