Use calculus to find the co-ordinates of the local minimum point of $f$.
- Leaving Cert Mathematics - Question c - 2021
Question c
Use calculus to find the co-ordinates of the local minimum point of $f$.
Worked Solution & Example Answer:Use calculus to find the co-ordinates of the local minimum point of $f$.
- Leaving Cert Mathematics - Question c - 2021
Step 1
Differentiate the function
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Answer
To find the local minimum point, we first differentiate the function f(x). The derivative can be represented as:
dxdf=6x−6
Step 2
Set the derivative to zero
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Answer
Next, set the derivative equal to zero to find the critical points:
6x−6=0
Solving this gives:
x=1
Step 3
Evaluate the function at the critical point
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Now, substitute x=1 back into the original function f(x) to find the corresponding y-coordinate:
f(1)=3−6+7=4
Step 4
Identify the local minimum point
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Answer
Thus, the co-ordinates of the local minimum point of f are:
(1,4)
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