Thread: Intro Calculus - Curve Sketching

Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions.

a) , when and

I don't know what to do... I'm used to sketching functions with equation questions and not interval questions....

Please show me a step by step solution to this question, thanks

Hello,

Originally Posted by Macleef

Sketch a graph of a function f(x) that is differentiable and that satisfies the following conditions.

a) , when and

I don't know what to do... I'm used to sketching functions with equation questions and not interval questions....

Please show me a step by step solution to this question, thanks

This means that in the part of the sketch where x<-3, the function will be increasing (derivative is positive). It will be the same for x>1.

Between -3 and 1, the function is, for example, decreasing.

Originally Posted by Moo

Hello,



This means that in the part of the sketch where x<-3, the function will be increasing (derivative is positive). It will be the same for x>1.

Between -3 and 1, the function is, for example, decreasing.

Why is the section between -3 and 1 decreasing? Isn't it increasing since f'(x) is greater than 0?? I'm confused...

Originally Posted by Macleef

Why is the section between -3 and 1 decreasing? Isn't it increasing since f'(x) is greater than 0?? I'm confused...

You said it was increasing for x<-3, that is to say to the left of -3, and for x>1, that is to say to the right of 1.

Between -3 and 1, you can choose

so it doesn't matter? would the graph look like a positive cubic function?

Originally Posted by Macleef

so it doesn't matter? would the graph look like a positive cubic function?

yeah, whatever... You're only asked that it increases in the given intervals.
As the question is formulated, the function is just not increasing between -3 and 1 (so it can be constant or decreasing)

thanks for the help... and I read the question wrong... there's actually more to it than that...