Differentiwtiom

Question 1

How to differentiate

Answer 1

Ultiply by power, subtract 1
3x = 3

3 = 0

Why?
3x0 basically so becomes 0

So yh

Question 2

If they say find equation of tangent on curve what to do

If normal?

Answer 2

Find gradient using differentiation sub in

2) normal grsdient is perpendicular so do thst then use known points

Question 3

What is an increasing or decreasing fucntion

Answer 3

When the grsdien is positive value of y is going up so increasing

When grsdient is negative value of y is going down so decreasing

So when grad >0 it’s increasing

Grad <0 it’s decreasing

Question 4

What are turning slash stationary poitns and maximum minimum imf,ectiom

Answer 4

Turning and stationary points is where the gradient ism0

Maximum is when the graidient is going from positive to 0 to negative

Min is negative tom0 to positive

Inflection is positive 0 positive or negative 0 negative

Question 5

How to draw gradient fucntion graoh

Answer 5

Basically stationary points are roots

And where grsdient is increasing, it has to just be positive on graoh and where gradient is decreasing just have to be negative that’s it

Question 6

Remmeber for negative and fractions

Answer 6

Same rule, negative means get SMALLER

Question 7

If second derivative negative

Posit be

But if it is 0, you just check ing method

Answer 7

Maximum

Else minimum

Because it is increasing rate of gradient

Question 8

Differentiate from fire torincipled

Answer 8

A point x, with function &(x) will have y coordinate f(x)

Now imagine point very close to x , x+( and y will be same as before

Basically to find an estimate of grsdient at xounfind avergwe grsdient between two values really close

And as h tends tpm0, this value gets more and more accurate the closer tom0 it is

Thatshow to fo

Question 9

MAKE SURE COORDINATES ARE CLEAR OTHERWISE YOU GINNA SHB IN BITH X INSTEAD OF X AND Y LMAO