It is given that at x = 1, the function x4−62x2+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.
It is given that at x = 1, the function x4−62x2+ax+9 attains its maximum value, on the interval [0, 2]. Find the value of a.
Solution and Explanation
Let f(x) = x4−62x2+ax+9.
f'(x)=4x3-124x+a
It is given that function f attains its maximum value on the interval [0, 2] at x = 1.
f'(1)=0
=4-124+a=0
a=120
Hence, the value of a is 120.
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Notes on Applications of Derivatives
Concepts Used:
Maxima and Minima
What are Maxima and Minima of a Function?
The extrema of a function are very well known as Maxima and minima. Maxima is the maximum and minima is the minimum value of a function within the given set of ranges.
There are two types of maxima and minima that exist in a function, such as:
- Local Maxima and Minima
- Absolute or Global Maxima and Minima