Question

The graph of a twice differentiable function is shown below. Order the values of f(2), f '(2), f " (2) in order from least to greatest. Explain your reasoning.

Answer 1

sorry sketch is not that great

Answer 2

I don't even know where to start with this one....

Answer 3

start at f(2) = 0

Answer 4

and notice that the graph is strictly increasing - what does that tell you about the first derivative ?

Answer 5

but isn't the graph given the second derivative

Answer 6

No the graph is between f(x) and x.

Answer 7

I thought "The graph of a twice differentiable function is shown below" meant the given graph is a 2nd derivative graph.

Answer 8

See, if a graph is strictly increasing as @ganeshie8 mentioned, its slope must be +ve (not even zero), so that its value never decreases.

Answer 9

Twice differentiable function means a function which can be differentiated twice.

For example: f(x) = x^3

Answer 10

ok so f(2)=0 f'(2)=+ f'(2)=-

Answer 11

f prime 2 is positive because f(x) is increasing
f double prime 2 is negative because f(x) is concave down

Answer 12

Yes. You can see from the graph that the slope at x = 2 was more than slope at x > 2, so, slope is obviously decreasing.

Or you can say that graph is concave down.

Answer 13

f(2)=0 because f(x) has a solution at (2,0)

Answer 14

Yes

Answer 15

Very good