Question

Between $ 1 $ and $ 2 $ , how many local maxima the function $ f (x) = 6x^5 - 7x^4 + 3x^3 + 2x^2 + 11 x - 17 $ has ?

• A. $ 0 $
• B. $ 1 $
• C. $ 2 $
• D. $ 3 $

Answer 1

Answer: (A)

We have, $f (x) =6x^{5}-7x^{4}+3x^{3}+2x^{2}+11x-17$
$f'(x) =30x^{4}-28x^{3}+9x^{2}+4x+11$
Here, $f' (x) >\, 0\, \forall \,x \, \in\left(1,2\right)$
$\therefore f (x)$ is an increasing function for $x \in\left(1,2\right)$
Thus, $f (x)$ has no local maxima $\forall\,x \, \in \left(1, 2\right)$