Question

Consider the function $f\left(x\right) = \frac{x^{3}}{4} - sin\,\pi x +3$

• 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

Answer: (B), (C)

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.