The Student Room Group

C1

f (x) = 2-x-x^3
Show that f (x) is decreasing for all values of x. (4 marks)
The mark scheme states:
dy/dx = -3x^2 -1
x^2 is greater than 0 for all real values of x.
*-1-3x^2 is less than or equal to -1.
Hence f (x) is decreasing for all values of x.
I don't understand why dy/dx is less or equal to -1.
Reply 1
find the range of values that f'(x) can take by completing the square or differentiating to find the turning point of the quadratic (negative x^2 coefficient, remember). If they're all negative, that means the gradient of f (x) is always negative.
(edited 5 years ago)
Original post by Chelsea12345
f (x) = 2-x-x^3
Show that f (x) is decreasing for all values of x. (4 marks)
The mark scheme states:
dy/dx = -3x^2 -1
x^2 is greater than 0 for all real values of x.
*-1-3x^2 is less than or equal to -1.
Hence f (x) is decreasing for all values of x.
I don't understand why dy/dx is less or equal to -1.


-3x^2 <= 0

And subtract one from each side.

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