Can anyone help me draw this? Its calc curve sketching

[wary rock]

Im just keep getting it wrong and I dont even have the answer sheet can someone draw the correct answer and explain to me like what's going on?

[tepid oar]

What specifically do you need help with?

[wary rock]

I don't understand how to use the signs of f'(x) and f''(x) to figure out where the graph is increasing or decreasing

or concave up and down

and im so confused with how the points like (3,5) (5,2) (7,-2) fit into that

[tepid oar]

Do you know what the derivative means?

[wary rock]

i only know its the slope of the tangent line

[tepid oar]

So, if the derivative is positive, that means the slope of the curve going through a certain point is positive

Same thing if the derivative is negative

It means the slope of the graph going through the point is negative

[wary rock]

ohhh ok that made it easier to understand

thank you

[devout jasper]

hi

[devout jasper]

this