need help with polynomials (1 Viewer)

[mountainchicken1103]

by considering its derivative, show that given polynomial B is always increasing. Hence, explain why it must have exactly one root. Then find an approximation of that root to 1 dp by using trial and error or another method

well i know the general answer for the question, as in the derivative must be positive to have it always increasing and that if its always increasing the graph only goes through the x axis once, but my teacher said I need a detailed explanation
thanks in advance

 

[CM_Tutor]

by considering its derivative, show that given polynomial B is always increasing. Hence, explain why it must have exactly one root. Then find an approximation of that root to 1 dp by using trial and error or another method

well i know the general answer for the question, as in the derivative must be positive to have it always increasing and that if its always increasing the graph only goes through the x axis once, but my teacher said I need a detailed explanation
thanks in advance

I agree with your teacher.

Consider your statement that "if its always increasing then graph only hoes through the x axis once"... is this true?

Consider a function like . Its derivative is always positive, it always increases, and yet it does not cross the -axis at all.

Now, what about ? Its derivative is always positive, it always increases, and yet it crosses the -axis infinitely many times.

What else do you need to observe about to conclude that it must cross the -axis, and that it can only do so precisely once?

 

[mountainchicken1103]

I agree with your teacher.

Consider your statement that "if its always increasing then graph only hoes through the x axis once"... is this true?

Consider a function like . Its derivative is always positive, it always increases, and yet it does not cross the -axis at all.

Now, what about ? Its derivative is always positive, it always increases, and yet it crosses the -axis infinitely many times.

What else do you need to observe about to conclude that it must cross the -axis, and that it can only do so precisely once?

thanks, this really helped