Question

I: The function $f\left(x\right)=9x^2-15x-x^3+10$ is increasing in $(1,5)$
II: The function $f\left(x\right)=9x^2-15x-x^3+10$ is decresing in $(1,5)$ Which of the above statements are true ?

• A. only $I$
• B. only $II$
• C. both $I$ and $II$
• D. neither $I$ nor $II$

Answer 1

The correct option is A only $I$

(I) $f^{\prime }\left(x\right)=18x-15-3x^2$
$=-3(x^2-6x+5)$
$=-3(x-5)(x-1)$
$f^{\prime }\left(x\right)>0$ $\forall xϵ(1,5)$