Question 8(b)
[Maximum number: 2]
Consider a function of the form , where b and c are constants. The graph of y=f(x) has a gradient of 0.208 at x=5.
Show that f(x) is increasing at x=3.5
IB Maths AI SL 5.2 Increasing and Decreasing Functions
Practise using the sign of a derivative to identify increasing or decreasing intervals and to justify whether a contextual quantity is rising, falling or meeting a rate constraint.
How this is tested
- evaluate or inspect f'(x) and link a positive or negative sign to local increase or decrease
- solve f'(x) > 0 or f'(x) < 0 and intersect the result with the stated domain
- compare a derivative or maximum rate with a contextual safety or performance threshold