5b Applications of Differentiation

Question 1

Equation of tangent to curve at P

given P [k, f(k)]

Answer 1

y - f(k) = f’(k) (x-k)

Question 2

Equation of normal to curve at P

given P [k, f(k)]

Answer 2

y - f(k) = 1/f’(k) (x-k), f’(k) ≠ 0

Question 3

Equation of tangent and normal to curve at P

if f’(k) = 0

Answer 3

y = f(k) - Horizontal Line
x = k - Vertical Line

Question 4

Rate of Change

Answer 4

1. Identify unknown variable.
2. Identify known variable(s).
3. If an unknown is in the given variable(s), substitute the unknown with something known, eg. substituting the height of a cylinder into the volume of the cylinder.
4. Connect variables using dy/dx = dy/du x du/dx with the unknown variable on the LHS.