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find greatest integer value of why fewer than 1000 x's. How to do?

Can someone give me a hint on how to solve this. I am at FP1 stage. I can use differentiation or some other method.

Question is What is the greatest integer x where y < 1000.

equation is:

y = \frac{1}{6}x(2x+1)(7x+1)

This is an inequality question?

Or do I just solve to get x value and nearest integer is answer?

How would I get started on this question?

(edited 9 years ago)

Reply 1

BabyMaths

You could solve

\frac{14x^3}{6}=1000

and then test a few x values.

Reply 2

Smaug123

Original post by acomber

Can someone give me a hint on how to solve this. I am at FP1 stage. I can use differentiation or some other method.

Question is What is the greatest integer x where y < 1000.

equation is:

y = \frac{1}{6}x(2x+1)(7x+1)

This is an inequality question?

Or do I just solve to get x value and nearest integer is answer?

How would I get started on this question?

Draw a sketch of y against x. That might help.

Reply 3

Hasufel

is this

y<1000x

y<1000

?

If the latter, then do what Smaug123 suggests..

If the former,i`d still do what Smaug123 suggests, but also put the 1000 on the LHS, expand, and re-factorise (dropping the 1/6) to give: