Question 42

The number of points where the function

$$f(x) = \begin{cases}(x + 1)^4 & x \leq 1\\(x - 5)^2 & x > 1\end{cases}$$ attains its local maximum is

Solution

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For $$x\le\ 1$$ the graph of the function is an upward parabola that attains its min at x = -1 and value is 0, at x = 1 its value is 16

Similarly for $$x>1$$ we see that its upward parabola which has value of 16 at x= 1 and decreases till x=5 at which its value is 0. After which the values increases again.

It can be seen local maxima is attained at x=1 only

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