Determining whether a curve is increasing or decreasing at a given point (1 Viewer)

[boongsta]

Determine whether the curve is increasing or decreasing at the given point:

a) y = x^4 - x^3 at (1,0)

b) y = 8x^2 + 11x - 4 at (-2,6)

c) y= -3/x at (3,-1)

thanks in advance

 

[insert-username]

Determine whether the curve is increasing or decreasing at the given point:

a) y = x^4 - x^3 at (1,0)

b) y = 8x^2 + 11x - 4 at (-2,6)

c) y= -3/x at (3,-1)

thanks in advance

If the curve is increasing, the derivative is positive. If the curve is decreasing, the derivative is negative. In these questions, derive the functions to find their gradient, then substitute in the x value given to find if its positive or negative. I'll do the first one:


a) y = x⁴ - x³ at (1,0)

dy/dx = 4x³ - 3x²

When x = 1, dy/dx = 4(1) - 3(1)

= 1

Therefore the curve is increasing as the derivative is positive.


I_F

 

[boongsta]

awesome thanks bruva I thought that was how you did it but I'm sure unsure of why they give us a y value ... whats the point

 

[insert-username]

awesome thanks bruva I thought that was how you did it but I'm sure unsure of why they give us a y value ... whats the point

It requires a little more intepretation. If they say "where x=2", that pretty easy, but if they say "at the point (2,5)", it makes you have to think that little bit more.


I_F

 

[boongsta]

Lol for no reason?

 

[SoulSearcher]

They do that to mess with your mind. Give you more information than you need and see whether you stuff up.