The maximum of the graph is (1.1, 0.9).
What is a maximum of the graph ?
"The maximum value of a graph is the point on the graph where the y-coordinate has the largest value. A maximum graph is one that represents the largest value of y-coordinate. There are two types of maximum values possible on a graph: a local maximum and an absolute maximum"
Given ,
Function is [tex]x^3 + x^2 - 6x + 5[/tex]
To find the maximum of the function we need to find the derivative of the function.
[tex]\frac{dy}{dt} = 3x^2 + 2x - 6 \\[/tex]
To find minima we have to put the derivative as 0
So, [tex]3x^2 +2x - 6 = 0[/tex]
using the root formula
x = 1.1 and -1.783
value of y corresponding to x = 1.1 is
[tex]y = x^3 + x^2 - 6x + 5 \\\\y = 1.1^3 + 1.1^2 - 6*1.1 + 5 \\\\y = 0.941[/tex]
So, the values at maximum of the graph is (1.1, 0.9).
Hence, A is the correct option.
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