LET’S LOOK AT SOME SIMPLE HINTS IN CALCULUS

1.WHEN FINDING THE DERIVATIVE FROM FIRST PRINCIPLES :

• step 1 : find (f(x+h)
• step 2 : find f(x+h) - f(x)
• step 3 : find  f(x+h) - f(x)

h

• step 4 : find lim     f(x+h) - f(x)

h -- 0        h

2. USING RULES OF DIFFERENTIATION

• if f(x) = ax  , then  f’(x) = n ax
• some conversions of f(x) before finding derivative ie. applying the above rule

a)  f(x) =           then  f(x) =  x 1/n

b)  f(x) =  (x-a) (x-b) , f(x) = x- xb - ax + ab

c)  f(x) =   c, f(x)  = c .

d) f(x) = (x + a)  , f(x) = x2 + 2ax + b2

• the derivative of a constant is zero eg  f(x) = 2 , f’(x) = 0

3. TANGENTS TO A CURVE

• if a tangent is drawn to a curve at a point (a,b) , then the gradient of the tangent  is given by f’a).
• the equation of the tangent : y - = m (x - )
• if y value is not given , then substitute x into f(x) to obtain y value

• eg find the equation of a tangent to the curve y = 2 -x at the point x=-2

4. THE CUBIC FUNCTION

• the cubic function has the general equation  :

f(x) = ax + bx+cx + d

indicates shape           y-intercept

• the graph of a cubic function has two stationary points called TURNING POINTS (local maximum and minimum ) as well as what is called a POINT OF INFLECTION.