Question

Let ƒ(x) = x³/4 – sin πx + 3. If ƒ(x) takes the value α on

[–2, 2] then α is equal to –

• A. 6
• B. –2
• C. 0
• D. 7/3

Answer 1

Answer: (D)

7/3

Answer 2

The function ƒ(x) = $\frac{x^{3}}{4}$ – sin πx + 3 is continuous within the interval [–2, 2]. Now ƒ(–2) = 1 and ƒ(2) = 5. By intermediate value theorem ƒ takes all values between 1 and 5. Thus ƒ takes the value α = 7/3.