Question

How were the answers 15 and -49 gotten?

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Answer 1

the maximum is at x=-1
you "put in" -1 for x in the equation
f(x) = 2x^3 - 6x^2 -18x + 5

in other words, you "erase the x" and replace it with -1:
2 (-1)^3 - 6(-1)^2 -18(-1) + 5

now it is arithmetic, but you have to remember order of operations
first do the exponents : (-1)^3 means -1* -1 *-1 = 1*-1 = -1
and (-1)^2 means -1*-1 = +1

2*-1 - 6*1 -18(-1) + 5
now do the multiplies:

-2 - 6 +18 + 5
now add: -8 + 18+5
10+5
15