Question

a
Suppose that f has a positive derivative for all values of x and that f(2) = 0. Which of the following statements must be true of the function

Answer 1

\[g(x)= \int\limits_{0}^{x}f(t) dt\]

Answer 2

A) The function g has a local maximum at x = 2.
B) The function g has a local minimum at x = 2.
C) The graph of g has an inflection point at x = 2.
D) The graph of g crosses the x-axis at x = 2.

Answer 3

but what if it isn't because the question says "of the function"

Answer 4

if there is a positive for all x doesnt that mean it never crosses x axis?

Answer 5

positive derivative means that the curve is proceeding in downward direction

Answer 6

oh

Answer 7

still think its d?

Answer 8

no no wait ..

Answer 9

i think its b,c,d ..
comments please :)

Answer 10

now im more confused

Answer 11

f(2)=0 implies that for f at x=2, y=0 thus option D is right.

Answer 12

you think its d sama?

Answer 13

Nothing can be said about the other options as there is no mention of the nature of the derivative of f except that it is +ve which implies f is always increasing in the domain.

So yes it is D :)

Answer 14

ok thanks sama and soul

Answer 15

hope its correct

Answer 16

Will be right ;) And you're welcome!

Answer 17

b..is correct sorry ..
see as

Answer 18

Dude I'm so sorry! I read g as f :P
B is right!