Answer to Question #185834 in Calculus for kaye

Question

𝑓(𝑥) = 𝑥

3 − 12𝑥, 𝑥 ∈ [0, 4]

Answer 1

Ans:- $f(x)=x^3-12x$ , $𝑥 ∈ [0, 4]$

$\Rightarrow$ $f(x)=x(x^2-12)\\$

$\Rightarrow f(x)=x(x+2\sqrt{3})(x-2\sqrt3)$

$\Rightarrow f(x)=x(x+3.4641)(x-3.4641)$

We know that $x$ lies in the interval between $𝑥 ∈ [0, 4]$.

Hence The values of $x$ for which $f(x)$ should be zero is $0, 3.4641$ and

$f'(x)=3x^2-12$

$\Rightarrow$ $f'(0)=-12<0$ so at $x=0$ the slope of the f(x) is increasing

$\Rightarrow f'(3.4641)=-5.5692<0$ so at $x=3.4641$ the slope of the $f(x)$ is increasing