Question

-

Answer 1

is it b? I am rust on my calc I

Answer 2

have't done those in years

Answer 3

those re in the book in a highlighted box to remember for sure

Answer 4

If f'(x)>0 on interval (a,b) that means the function is increasing on (a,b). Consequentialy, if f''(x)>0, then the slope (f'(x)) is increasing on (a,b).

Answer 5

because f" in relation to f' is same as f' in relation to f.
(one way to think about it)

Answer 6

So A would have been true, if it sais "concave up".

Answer 7

[option B]
If f '(x) > 0 on the interval (a, b) then f(x) is increasing on the interval (a, b).

The slope is greater than zero, so yes, the function is increasing on that interval.

Answer 8

just remember, the derivative is just a instantaneous rate of change, the slope of a tangent line to a curve... that should work

Answer 9

+ derivative, the function has positive sloped tangents, it must be going upwards

Answer 10

If f '(c) = 0, then x = c is a relative maximum on the graph of f(x).

Not necessarily!
Could be absolute minumum for example.

Answer 11

is that most of calc,

how the heck do you calculate a slope of a line with 1 point

Answer 12

What do you realy mean?

Answer 13

infinitesmals i guess

a distance vanashing, so really you have a slope from one point, maybe

Answer 14

(If I am interpreting the question correctly, if not nvm)
We are considering the case in option C as given.

Answer 15

If you have any questions ask them piz.

Answer 16

Oops, "pliz".

Answer 17

If f '(c) = 0, then the following is possible (only one can happen)

* there is a relative min on f(x) at x = c
* there is a relative max on f(x) at x = c
* there is a saddle point on f(x) at x = c. A saddle point is a place where the tangent line has a slope of 0, but it's not a min or max

this is why you have to use the first or second derivative test to figure out if there is an extrema at x = c

Answer 18

thanks!!