Q115 / 155 · WBJEE 2019 · Mathematics
Consider the function $f(x)=\frac{x^{3}}{4}-\sin \pi x+3$
- A$f(x)$ does not attain value within the interval [-2,2]
- Correct answerB$f(x)$ takes on the value $2 \frac{1}{3}$ in the interval [-2,2]
- Correct answerC$f(x)$ takes on the value $3 \frac{1}{4}$ in the interval [-2,2]
- D$f(x)$ takes no value $\rho, 1 < p < 5$ in the interval [-2,2]
Solution
\(f(-2)=1\) and \(f(2)=5\) and \(f\) is continuous also.
So intermediate value theorem, function \(f(x)\) takes all values between 1 to 5 .
\(\Rightarrow \quad 2 \frac{1}{3}\) and \(3 \frac{1}{4}\) lies in 1 to 5 so option \(B, C\) are correct
Hence, the correct answer is options: 'B', 'C'.