Summary Math Metacog finding the gradient at a point Calculus

finding Gradient at a Point
Di erentiation


● Use this when you need to find gradient at a point
● Gradient is also known as Derivative it can be denoted as ‘
Eg ; F’(x)




Long Method


Only use it when it says…


● From first principles
● Using the definition
● Using method of limits
● Using h method


…then the derivative must be found using


F ‘ (x) = lim f (x + h) - f (x)
h➡0 h


Steps ;


1. Factorise (get h out of the denominator)
2. Sub in the limit
3. Simplify
4. Most likely your answer will be in terms of x

, The question could also say, at the point where x = 3



5. After you simplify your answer, f(x) = answer
6. Fill in the 3 in its whenever there's an x
7. f(3) = answer




Short Method

Use this always unless instructed di erently…



For example ;
F (x) = 4x2 - x3 - 2


1. Multiply exponent to coe cient
2. Minus one from exponent
3. If it’s a constant then make it 0


4x2 = 8x
- x3 = -3x2
-2=0


∴ F (x) = 8x - (-3x2)