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  • The function <img alt="\mathrm{f(x)=\frac{x^{3}}{8}-\sin \pi x+4}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bf%28x%29%3D%5Cfrac%7Bx%5E%7B3%7D%7D%7B8%7D-%5Csin%20%5Cpi%20x&amp

The function \mathrm{f(x)=\frac{x^{3}}{8}-\sin \pi x+4} in \mathrm{[-4,4]} does not take the value

Option: 1

-4


Option: 2

10


Option: 3

18


Option: 4

12


Answers (1)

best_answer

\mathrm{f(x)=\frac{x^{3}}{8}-\sin \pi x+4}
\mathrm{f(-4)=-4, f(4)=12}

\mathrm{\Rightarrow f(x)} can take value 10 as \mathrm{ f(x)} is continuous function
\mathrm{ \frac{x^{3}}{8}+4 \leq 12\, and \, I \sin \pi x \mid \leq 1 \forall x \in[-4,4]}

\mathrm{ \therefore f(x)}  cannot take the value 18

Posted by

seema garhwal

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