Differentiation (Increasing and Decreasing Functions)

[@silverorange0332]

How do you know when to factorise and when to complete the square ?

[@invincible_rl2562]

it’s completing the square when the question asks for the turning point of a graph, or when it says give the answer in the form (x+a)^2 +b. it’s factorising if the question says solve. or work out the x intercepts, or work out the solutions to a graph

[@twopolaar599]

Also, just to add, if you cant factorise with factors then you can resort to completing the square or other methods

[@hamzah7]

Cheers

[@StarPlaysRoblox13]

Why cant it be 0 is greater than "and equal to" x..etc.. Is it bcuz of dy/dx < 0?

[@Leo-tv4mt]

what if you have to work out the values of x for the function y= 2x-3 which is increasing?

[@1stClassMaths]

All values. dy/dx = 2 > 0 (Its also a straight line graph so if you think about the graph its always increasing)

[@Leo-tv4mt]

@@1stClassMaths makes sense, thank you

[@Sidaferrrr]

[@subhanawan6763]

what if the dy/dx is a quadratic eq and the its equal to zero? E.g 128x^2 +125x+1000 for x>0. Is it increasing/decreasing/neither ?

[@1stClassMaths]

128x^2 +125x+1000 is > 0 for all values of x so the function is always increasing.

[@subhanawan6763]

@@1stClassMaths how about the same equation being equal to zero, i.e. f'(x)= 128x^2 +125x+1000=0 for x>0 where f'(x) is dy/dx of another equation.Then what should we do?

[@1stClassMaths]

That function cannot be equal to 0 for any x value. It is always positive.

[@subhanawan6763]

@@1stClassMaths thanks

[@AlistairWallman]

what is a critical value?

[@1stClassMaths]

kzbin.info/www/bejne/eJ3LhpyMZpWNebM

[@salamisupplier]

for q1, would 0 < x < 2/3 still be correct or only x

[@1stClassMaths]

Only < 2/3 since negative values are still ok.

[@s2_krysp1]

I believe it is incorrect from 4:39 onwards for the final example

[@s2_krysp1]

Im not sure though

[@1stClassMaths]

I don’t think so it looks ok to me. What do you think it wrong?

[@s2_krysp1]

@@1stClassMaths At first, I thought it was wrong because it's for decreasing and I thought that the values below 0 had both decreasing and increasing, since it decreases to a minimum point, but then rises up. In short, I thought the decreasing part would be the left hand side of the graph, not the part below 0

[@1stClassMaths]

Ah ok. Remember it isn’t when this graph is decreasing but the graph of the original function. If you graph the cubic it doe decrease from 0 to 2.

[@EE-Spectrum]

Actually, for a decreasing function, it's where the gradient of the graph is negative or less than zero. It's not where it is below the x-axis. Below the x-axis tells where the graph is negative and not where the gradient is negative. Actually, the gradient could be negative above the x-axis as well.

[@kebabz5856]

can you be muine