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Let h(x) = f ( x ) - [ f(x)]2 + [f(x)3 for every real num ber x, then
  • a)
    h is increasing whenever f is increasing.
  • b)
    h is increasing whenever f is decreasing.
  • c)
    h is decreasing whenever f is decreasing.
  • d)
    nothing can be said in general.
Correct answer is option 'A,C'. Can you explain this answer?
Verified Answer
Let h(x) = f ( x ) - [ f(x)]2 + [f(x)3for every real num ber x, thena)...
Let h(x)= f (x) - [f(x)]2 + [f(x)]3
Differentiate the whole equation write to x, we get


So, h(x) is increasing function if f(x) is increasing function and h(x) is decreasing function if f(x) is decreasing function.
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Most Upvoted Answer
Let h(x) = f ( x ) - [ f(x)]2 + [f(x)3for every real num ber x, thena)...
Let h(x)= f (x) - [f(x)]2 + [f(x)]3
Differentiate the whole equation write to x, we get


So, h(x) is increasing function if f(x) is increasing function and h(x) is decreasing function if f(x) is decreasing function.
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Let h(x) = f ( x ) - [ f(x)]2 + [f(x)3for every real num ber x, thena)h is increasing whenever f is increasing.b)h is increasing whenever f is decreasing.c)h is decreasing whenever f is decreasing.d)nothing can be said in general.Correct answer is option 'A,C'. Can you explain this answer?
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