Why is this true:
Wouldn't it be 1 real zero?
Example says:
If function is strictly increasing on interval (a,b), then f has exactly one real zero in [a,b]. Note: f(a) and f(b) have opposite signs.
If function is strictly decreasing on interval (c,d), then f has exactly one real zero in [c,d]. Note: f(c) and f(d) have opposite signs.
_____
Our function is strictly increasing on (1,3), so it has exactly one real zero in [1,3]. Note: f(1) and f(3) have opposite signs.
Our function is strictly decreasing on (3,4), so it has exactly one real zero in [3,4]. Note: f(3) and f(4) have opposite signs.
Hence, our function has exactly two real zeros in the interval [1,4].
Last edited by parad0xica; 21 Apr 2016 at 6:23 PM.
Why can't I know this if I'm in high school?
The concepts used in this question can be understood by anyone. It's just that the mathematical language can be frightening and difficult to comprehend but when a diagram pops up, the tunnel will become clear
Not sure I'm a primary school or high school student or something else.. up to you to deduce and decide :P
Last edited by parad0xica; 21 Apr 2016 at 6:49 PM.
Why are the first 2 answers not correct?
g'(x) = 3x-24x+45, so g(2) = 3 right?
and
h'(x) = ln(x-1), so h(2) = 0 ?
Or am I doing something wrong here?
Where is the mathsoc solutions to the calculus test 2 past papers??? I can find the solutions for every other test just not calc test 2??
Pls help.
Just confirming I'm correctly using the definition of the derivative:
So to show that f(x) = x^2 then f'(x) = 2x, you get the formula, sub in and after expanding and simplifying you get 2x+h. Now as h -> 0, h = 0, so we make h = 0 and then we are left with 2x.
Is this how you use it? I.e. finding the limit as h -> 0, which is 0...? or???
f(x) = x|x|
If it exists, evaluate lim h->0+ [f(0+h) - f(0)] / h
What do I even do here? Why have they got 0 already in the formula?
They want you to find lim h->0 f'(0)
Note that x=0 does not strictly imply the same thing as h=0
Also note that f(0) = 0
So if you want to find lim h->0^{+} f(h)/h
Note that as h approaches 0 from the right, x = x and |x| = x
(Instead if h approaches from the 0 left, x = x but |x| = -x)
So they want you to see if there's an answer to lim h->0^{+} h|h|/h
(Apologies for poor wording)
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