How do you find the range of #f(x)=5x^2+2x-1#?

1 Answer
dani83
Aug 14, 2015

Range: #{f(x) in RR: f(x) >= -6/5} #

Explanation:

# f(x) = 5x^2 + 2x - 1 #

Method 1: Completing the squares
# f(x)= 5(x^2 + 2/5x + 1/25 - 1/25) - 1 #
# = 5(x + 1/5)^2 - 6/5 #

Method 2: Stationary points
# f'(x)= 0 #
# 10x = -2 #
# x = -1/5, f(-1/5) = -6/5 #

Minimum point #(-1/5,-6/5)#

Hence range: #{f(x) in RR: f(x) >= -6/5} #

graph{5x^2+2x-1 [-2, 2, -5, 5]}

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