WBJEE · Maths · Differentiation
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]
- B \(f(x)\) takes on the value \(2 \frac{1}{3}\) in the interval [-2,2]
- C \(f(x)\) 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]
Answer & Solution
Correct Answer
(C) \(f(x)\) takes on the value \(3 \frac{1}{4}\) in the interval [-2,2]
Step-by-step Solution
Detailed explanation
\(f(-2)=1\) 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
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