What is the value of (X) for which the function f(X)=2x^3-9x^2+12x+2 is decreasing
Answers
Answer:
which standard are you in.
Answer:
given: f(x) = 2x³ - 9x² + 12x + 2
to know the value of x at which the given function is decreasing
f'(x) = 6x² - 18x + 12
equate f'(x) to zero to find the critical point
6x² - 18x + 12 = 0
x² - 3x + 2 = 0
x² - 2x - x + 2 = 0
x(x - 2) - 1(x - 2) = 0
x - 1 = 0, x = 1
x - 2 = 0, x = 2
therefore at x = 1 and x = 2 the slope is zero, hence these two points are the critical points
____0_____+____1____-___2____+____3
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let us check a point to the left of x = 1
let x = 0
f'(0) = 6*0² - 18*0 + 12 = 12 > 0
let us check a point between 1 and 2
f'(1.5) = 6*(1.5)² - 18*(1.5) + 12
=> 6*(2.25) - 27 + 12
=> 13.5 - 27 + 12 => - 1.5 < 0
let's check to the right of x = 2
f'(3) = 6*3² - 18*3 + 12
=> 54 - 54 + 12 = 12 > 0
therefore from the above test, the function decreases in the interval ( 1, 2 )