SOLUTION: Find the difference quotient F(x)= 5x - x^2 F(5 +h)

SOLUTION: Find the difference quotient F(x)= 5x - x^2 F(5 +h) - f(5)

Question 655272: Find the difference quotient
F(x)= 5x - x^2
F(5 +h) - f(5)
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Find the difference quotient
F(x)= 5x - x^2
F(5 +h) - f(5)
.
First, find F(5+h):
F(5+h) = 5(5+h) - (5+h)^2
F(5+h) = 25+5h - (5+h)(5+h)
F(5+h) = 25+5h - (25+10h+h^2)
F(5+h) = 25+5h -25-10h-h^2
F(5+h) = 5h-10h-h^2
F(5+h) = -5h-h^2
F(5+h) = -h^2-5h
.
Find, F(5):
F(5)= 5(5) - (5)^2
F(5)= 25 - 25
F(5)= 0
.
So,
F(5 +h) - f(5) = -h^2-5h-0
F(5 +h) - f(5) = -h^2-5h

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