Differentiation roots of equations

Question 1

What is the second derivative and what does it show?

Answer 1

d^2y/dx^2

• If second derivative is greater than >0 local minimum point.
• If second derivative is less than <0 local maximum
• If second derivative = 0 point of inflexion but must see change of sign

Question 2

What happens if second derivative = 0?

Answer 2

could be point of inflexion, local or max.

Question 3

How does differentials link to concave and convex functions?

Answer 3

• Concave when f’‘(x) <0

- Convex when f’‘(x) > 0

Question 4

How to differentiate functions in the form a(x+1)^N

Answer 4

• Chain rule
• Step 1 multiply the derivative of the bracket
• Step 2 multiply the power
• Step 3 reduce the power by one.

Question 5

How do differentiate functions in the form 3xe^x

Answer 5

• Product rule
• Let one function = u and the other v
• Then do U dv/dx + V du/dx

Question 6

How to differentiate functions in the form f(x) / g(x)

Answer 6

Quotient rule

-in the formula booklet

Question 7

How to differentiate implicitly?

Answer 7

-differentiate x as normal and then when differentiating y multiply by dy/dx.
Then make dy/dx the subject.