A function, f, is defined on the set of real numbers by f(x) = x³ - 7x - 6 - Scottish Highers Maths - Question 3 - 2018
Question 3
A function, f, is defined on the set of real numbers by f(x) = x³ - 7x - 6.
Determine whether f is increasing or decreasing when x = 2.
Worked Solution & Example Answer:A function, f, is defined on the set of real numbers by f(x) = x³ - 7x - 6 - Scottish Highers Maths - Question 3 - 2018
Step 1
Differentiate f
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Answer
To determine whether the function f is increasing or decreasing, we first need to find the derivative of the function:
f′(x)=3x2−7
Step 2
Evaluate derivative at x=2
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Answer
Next, we evaluate the derivative at x = 2:
f′(2)=3(2)2−7=3(4)−7=12−7=5
Step 3
Interpret result
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Answer
Since the derivative at x = 2 is positive (5 > 0), this indicates that the function f is increasing at this point. Therefore, we conclude that f is increasing when x = 2.
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