Question

Sketch the graph of a differentiable function f that satisfies the given conditions.

f(3) = 5; f(5) = 0; f'(3)=f'(5)=0;
f'(x) > 0 if x<3 or x>5; f'(x) < 0 if 3 14 years ago

Answer 1

seems pretty easy

Answer 2

Not to me. :P

I can obviously plot the points (3,5) and (5,0), but the two x-intercepts should be (2,0) and (5,0). I can see (5,0), but where is (2,0) coming from?

Answer 3

ill try some rough sketches on paint.

Answer 4

Hey elcengineer, save you some trouble. I have the answer in the back of my book.

The issue is with HOW to get the answer. I've mentioned the x-intercepts...5 makes sense...but where is 2 supposed to come from?

Answer 5

really rough , only took 1 minute

Answer 6

its obviously a cubic

Answer 7

the two has most likely been randomly chosen

Answer 8

it makes no difference, all it says is draw a graph that follows the conditions given, there are infinitely many graphs that follow the conditions , and one of them will have an x intercept of 2.

As long as you have the general shape that is all they are after

Answer 9

and the x intercept must be less than 3, obviously, or it obviously wrong geometrically, but you wouldnt need to give an x intercept anyway.

Answer 10

it is art

Answer 11

Thanks a bunch! Here I am going through the entire darn section looking for the solution and you just gave it to me! So they could have chosen ANY number less than 3 as the x-intercept then and would have just widened the graph? It would still be the correct answer? Even if you don't reply, "Good Answer"!

Answer 12

I dont know if you could pick any value for the x , because if you were to pick something very close to 3, infinitely close to 3 , then you would have jaggered edges and it wouldn't be differentiable, so it would kinda violate the condition.

but still, theres no need to worry bout that, they arent testing that in the question, they jsut want general shapes.

Answer 13

Yeah, I should have clarified. Something within the vicinity of 3-x with x being a small number.

Answer 14

just dont worry bout it

Answer 15

OK. Thanks!