Question

Find the Range of f(w)= 2w^2+w-1 and g(w)=w^2-(underoot)w-1

Answer 1

\[f(w)=2w ^{2}+w-1 and g(w)=w ^{2}-\sqrt{w-1}\]

Answer 2

@Hannahsayshi

Answer 3

How to find the Range

Answer 4

Okay I'm going to tag my friend okay

Answer 5

OK :)

Answer 6

@A_Burning_Masquerade

Answer 7

Give me two minutes tops

Answer 8

OK Sir!

Answer 9

Okay when I do the math the answer comes out differently then when I check it. I really don't know because I'm usually not wrong and I don't want to give you the wrong answer. So could @TheSmartOne help out.

Answer 10

find x for f'(x)=0. Plug it in f(x) and evaluate the range

Answer 11

Can you do it?

Answer 12

OK Faiq how am I supposed to do that can u please explain

Answer 13

So there are two methods for you question. One is simply drawing a graph to evaluate it out and second is calculus (the cool one). Which method do you opt for?

Answer 14

Its OK np @A_Burning_Masquerade Thanks for trying to help me out

Answer 15

calculus :)

Answer 16

So first you've to understand what the notation implies.
f(x) means something described in the terms of x or you can say a function of x
f'(x) or \(\large\rm \frac{d}{dx}f(x) \) implies the change in rate of f(x) with respect to x. Are you clear on that?

Answer 17

yeah its clear Thanks

Answer 18

So \(\large\rm \frac{d}{dx}f(x)\) implies the change in f(x). Now the change can be positive. Meaning for increasing values of x, the output is increasing. Or the change could be negative. Meaning for increasing values of x, the output is decreasing. But a special case comes at 0. When\(\large\rm \frac{d}{dx}f(x)=0\) it means that on that very x coordinate, the \(\large\rm f(x)\) has gone from decreasing to increasing or from increasing to decreasing. Clear on that?

Answer 19

yes sir

Answer 20

Now notice the graph of \(\large\rm f(x)\)when \(\large\rm \frac{d}{dx}f(x)=0\)

Can you point out by drawing a line which is the lowest point for f(x)?