Asked by beavis
The question says : the gradient of a curve is give by dy/dx = x^2 - 6x. Find the set of values of x for which y is an increasing function of x.
I didn't understand what they are asking me to do could you solve and explain?
I didn't understand what they are asking me to do could you solve and explain?
Answers
Answered by
Reiny
You want x^ - 6x to be positive, so
x^2 - 6x > 0
x(x-6) > 0
so the critical values of x are 0 and 6
look at a number < 0 , say x = -1
your statement is -1(-7) > 0 , which is TRUE
look at a number between 0 and 6, say x=4
your statement is 4(-2) > 0 , which is FALSE
look at a number > 6, say x = 10
your statement is 10(4) > 0 , which is TRUE
so x must be less than 0 OR greater than 6
your function increases for
x < 0 OR x > 6
x^2 - 6x > 0
x(x-6) > 0
so the critical values of x are 0 and 6
look at a number < 0 , say x = -1
your statement is -1(-7) > 0 , which is TRUE
look at a number between 0 and 6, say x=4
your statement is 4(-2) > 0 , which is FALSE
look at a number > 6, say x = 10
your statement is 10(4) > 0 , which is TRUE
so x must be less than 0 OR greater than 6
your function increases for
x < 0 OR x > 6
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.