Question

The minimum value and maximum value of the function a² - 2a + 10 in the period 0 ≤ a ≤  5 are P and Q respectively. What will be the sum of P + Q?
1. 16
2. 25
3. 34
4. 41

Answer 1

Correct Answer - Option 3 : 34

Calculation:

f(a) = a2 - 2a + 10

f^|(a) = 2a - 2 = 0

⇒ a = 1

Function f(a) decreases upto a = 1, ∵ f^|(a) is negative for a < 1.

Function f(a) increases from a = 1, ∵ f|(a) is positive for a > 1.

f(a) is minimum at a = 1 and maximum at a = 5.

f(1) = 1² - (2 × 1) + 10 = 9

f(5) = 5² - (2 × 5) + 10 = 25

f(1) + f(5) = 9 + 25 = 34

• A quadratic function represented in a graph as a parabola.
• Depends upon the coefficient of x² it can be an upward one or a downward one.
• Here a is positive, therefore it is an upward parabola.