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:

Maxima and minima are known as the extrema of a function.

Maxima and minima are the maximum or the minimum value of a function within the given set of ranges

Let f (x) = x⁴ - 62x² + ax + 9

Therefore,

On differentiating wrt x, we get

f' (x) = 4x³ - 124x + a

It is given that function f attains its maximum value on the interval [0, 2] at x =1.

Hence,

f' (1) = 0

⇒ 4x³ - 124x + a = 0

⇒ 4 - 124 + a = 0

⇒ - 120 + a = 0

⇒ a = 120

Thus, the value of a = 120

---

NCERT Solutions Class 12 Maths - Chapter 6 Exercise 6.5 Question 11

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

Summary:

The value of a is 120 for the  function x⁴ - 62x² + ax + 9 that attains its maximum value, on the interval [0, 2]. Maxima and minima are known as the extrema of a function