Question

Ricardo throws a stone off a bridge into a river below. The stone's height (in meters above the water), xxx seconds after Ricardo threw it, is modeled by w(x)=-5(x-8)(x+4)w(x)=−5(x−8)(x+4)w, left parenthesis, x, right parenthesis, equals, minus, 5, left parenthesis, x, minus, 8, right parenthesis, left parenthesis, x, plus, 4, right parenthesis What is the maximum height that the stone will reach?

Answer 1

For this case we have the following function:
 w (x) = - 5 (x-8) (x + 4)
 Rewriting we have:
 w (x) = - 5 (x ^ 2 + 4x - 8x - 32)
 w (x) = - 5x ^ 2 - 20x + 40x + 160
 w (x) = - 5x ^ 2 + 20x + 160
 Then, deriving we have:
 w '(x) = - 10x + 20
 We equal zero and clear x:
 0 = -10x + 20
 10x = 20
 x = 20/10
 x = 2 seconds
 Substituting values:
 w (2) = - 5 (2-8) (2 + 4)
 w (2) = - 5 (-6) (6)
 w (2) = 180 meters
 Answer:
 The maximum height that the stone will reach is:
 w (2) = 180 meters