11Second o Derivative negative means that its maxima but A function can have many local maxima and minima. For such sums we check whether the function is decreasing or increasing and then apply the values of the range .
The largest value of 2x3 -3x2-12x+5 for -2≤x≤4 occurs at x equals
A. -2
B. -1
C. 2
D. 4
By normal maxima calculation im getting B,but ans given is D.
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7 Answers
11dy/dx = 6x2 - 6 x -12
dy/dx = 0
x2-x -2 = 0
x = (1 ± 3)/2
x = 2, -1
On drawing the number line we get that from 2 to ∞ the function is increasing therefore the maxima will be at 4
11but virang second derivative with x=-1 is coming negative..so shudnt fn. be max. at -1.
11
341@ronald: when you find an extremum point, say a maximum, it is more accurately called a local maximum. It does not mean it is the maximum over the entire domain of the function.
Like in this case, it is easy to see that as x→∞, f(x) →∞ and likewise as x→ - ∞, f(x) → - ∞.
So, you will ask what does it mean to say that x = -1 is a maximum.
It only means that there exists an interval I containing x=-1 such that for all x \in I - \{-1 \}, f(x) < f(-1).
11Thx prophet Sir for explaining y do u call it maximum. This had been my doubt too