This is the right approach. ##p## and ##m## are both positive, so you can work out where the slope ##dy\over dx## is negative.Natasha1 said:
Am I correct then when I write this?BvU said:
And check this last stepNatasha1 said:
!You have a range for ##x##. Let's write ##a = m/3p##, so that ##a## is some positive number. We have the equation $$x^2 < a$$ What does that say about ##x##? Try drawing a graph of the function ##x^2##, with the line ##y = a## marked.Natasha1 said:
No. You have an inequality. Inequalities typically have a range of solutions.Natasha1 said:
Let's assume ##a = 1##. What does ##x^2 < 1## tell you?Natasha1 said:
Is that what you see on your graph?Natasha1 said:
I recognise your problems with these concepts. You may want to consider a private tutor if grasping the basics of mathematics is important to you. We may not be able to do enough on a forum like this. I can't stand over you and help you draw a graph, for example.Natasha1 said:
Let me give you a basic result of mathematics: $$x^2 < 1$$ is equivalent to $$-1 < x < 1$$Natasha1 said:
Yes.Natasha1 said:
A negative gradient is a measure of the slope or steepness of a curve. It indicates that the curve is decreasing from left to right, meaning that the y-values are getting smaller as the x-values increase.
To find the range of values of x where a curve has a negative gradient, you can graph the curve and visually identify where the slope is negative. Alternatively, you can take the derivative of the curve and set it equal to a negative value, then solve for x to find the range of values.
No, a curve cannot have a negative gradient at only one point. A negative gradient indicates that the curve is decreasing over a range of values, not just at a single point.
A negative gradient tells us that the curve is decreasing, or getting smaller, as the x-values increase. This can indicate a downward trend or a decrease in the rate of change.
A negative gradient can indicate a concave down curve, where the slope is decreasing as the x-values increase. However, a negative gradient alone does not necessarily determine the concavity of a curve, as it also depends on the rate at which the slope is decreasing.