curve sketching help (1 Viewer)

[petergriffin198]

hey guys for this question, i know how to find the horizontal asymptote, i know its symmetrical about the y axis, i know it doesnt go below the x axis the origin and i know as x approaches plus-munis infinity, y approaches 2 but how do you determine the shape?

 

[kawaiipotato]

That's basically all you need. Except since you know it's reflected about the y-axis, see where it lies ON the y-axis. Sub x = 0, gives you y = 0. So it starts at origin. Unsure how to explain this part, but it has to be a stationary point at the origin, as symmetrical and differentiable curves like this don't have a critical point at the point of symmetry. I may be wrong tho. You'd verify this by calculus, but the question said not to use it so just do it on a spare piece of paper

 

[petergriffin198]

That's basically all you need. Except since you know it's reflected about the y-axis, see where it lies ON the y-axis. Sub x = 0, gives you y = 0. So it starts at origin. Unsure how to explain this part, but it has to be a stationary point at the origin, as symmetrical and differentiable curves like this don't have a critical point at the point of symmetry. I may be wrong tho. You'd verify this by calculus, but the question said not to use it so just do it on a spare piece of paper

got it, thanks

 

[petergriffin198]

That's basically all you need. Except since you know it's reflected about the y-axis, see where it lies ON the y-axis. Sub x = 0, gives you y = 0. So it starts at origin. Unsure how to explain this part, but it has to be a stationary point at the origin, as symmetrical and differentiable curves like this don't have a critical point at the point of symmetry. I may be wrong tho. You'd verify this by calculus, but the question said not to use it so just do it on a spare piece of paper

got it, thanks.
oh but what do u mean by "critical pt"?

 

[kawaiipotato]

got it, thanks.
oh but what do u mean by "critical pt"?

A critical point is when the gradient of the tangent is undefined or "vertical". An example would be at the point (0,0) for y = sqrtx . It initially starts vertical at the origin

 

[Trebla]

A critical point is when the gradient of the tangent is undefined or "vertical". An example would be at the point (0,0) for y = sqrtx . It initially starts vertical at the origin

A critical point also includes points where the derivative is zero.