Question

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 \(p, 1<p<5\) in the interval \([-2,2]\)

Answer 1

Ans : (B, C)
Hint \(: f(-2)=1\) and \(f(2)=5 \quad\) Also \(f\) is continuous.
Therefore by Intermediate value theorem, function f takes all values between 1 to 5 .