Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
If the function =\frac{a x+b}{(x-1)(x-4)} \) has a local maxima at , \) then
If the function \( f(x)=\frac{a x+b}{(x-1)(x-4)} \) has a local maxima at \( (2,-1), \) then
- A. \( b=1, a=0 \)
- B. \( a=1, b=0 \)
- C. \( b=-1, a=0 \)
- D. \( a=-1, b=0 \)
Step-by-step solution
Given f(2)=-1 yields 2a+b=2. f'(2)=0 yields b=0, so a=1. Thus a=1, b=0.
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