A polynomial function $f(x)$ is such that $f'(4)=f''(4)=0$ and f(x) has minimum value 10 at x = 4. Then,
Answer & explanation
Correct answer: option 2
We have,
$f^{\prime}(4)=0$ and $f^{\prime \prime}(4)=0$.
∴ $f(x)=(x-4)^n+\lambda$, where $n \geq 3$.
It is given that $f(x)$ has minimum at $x=4$. Therefore, $n=4$.
So, $f(x)=(x-4)^4+\lambda$
Now, $f(4)=10 \Rightarrow 10=\lambda$
Hence, $f(x)=(x-4)^4+10$