IB Maths Studies Differentiation
Questions and Answers
1. IB Mathematical Studies SL – Derivatives
How can we find the derivative of the following functions?
Solution
IB Mathematical Studies SL – Derivatives
2. IB Mathematical Studies SL – Differentiation
How can we find the derivative of the following functions?
Solution
IB Mathematical Studies SL – Derivatives
So the derivative function will be
So, the derivative function will be
3. IB Mathematical Studies SL – Differentiation, Gradient of the tangent
How can we find the gradient of the tangent to at
?
Solution
IB Mathematical Studies SL – Derivatives, Gradient of the tangent
Firstly we have to simplify the function
Secondly, we have to calculate the derivative function
And finally plug-in the value in order to find the gradient of the tangent to the curve at this point
4. IB Mathematical Studies SL – Differentiation, Equation of the tangent
How can we find the equation of the tangent to at
?
Solution
IB Mathematical Studies SL – Derivatives, Equation of the tangent
Firstly we have to simplify the function
Secondly, we have to calculate the first derivative function
Then we have to plug-in the value in order to find the gradient of the tangent to the curve at this point
Since the contact point is
.
Therefore the equation of the tangent to the curve at
has equation:
5. IB Mathematical Studies SL – Differentiation, Second derivative
How can we find the second derivative of the following functions?
Solution
IB Mathematical Studies SL – Derivatives, Second derivative
Firstly we have to simplify the function
So, the first derivative function is:
and the second derivative is:
Similarly,
The first derivative function is
and the second derivative is:
6. IB Mathematical Studies SL – Differentiation, Monotonicity, Increasing Decreasing Function
How can we find the intervals where is decreasing or increasing?
Solution
IB Mathematical Studies SL – Derivatives, Monotonicity, Increasing Decreasing Function
Firstly, we have to find the first derivative function
which is positive in the intervals
and is negative in the interval
Therefore the function is increasing for
and is increasing for