hw 15 - increasing and decreasing functions section 3.1: prob (1 point) find the critical value(s) of the…

hw 15 - increasing and decreasing functions section 3.1: prob (1 point) find the critical value(s) of the function $f(x)=17xln x$. $x_0 = square$ (leave your answer exact or round to three decimal places.) you have attempted this problem 0 times. you have 6 attempts remaining. email instructor

hw 15 - increasing and decreasing functions section 3.1: prob (1 point) find the critical value(s) of the function $f(x)=17xln x$. $x_0 = square$ (leave your answer exact or round to three decimal places.) you have attempted this problem 0 times. you have 6 attempts remaining. email instructor

Answer

Explanation:

Step1: Find the derivative

Use the product - rule $(uv)' = u'v+uv'$, where $u = 17x$ and $v=\ln x$. $u' = 17$ and $v'=\frac{1}{x}$. So $f'(x)=17\ln x + 17x\cdot\frac{1}{x}=17\ln x + 17$.

Step2: Set the derivative equal to zero

Set $f'(x)=0$, so $17\ln x+17 = 0$. First, subtract 17 from both sides: $17\ln x=-17$. Then divide both sides by 17: $\ln x=- 1$.

Step3: Solve for x

Since $\ln x=-1$, and $\ln x = \log_e x$, then $x = e^{-1}=\frac{1}{e}\approx0.368$.

Answer:

$\frac{1}{e}\approx0.368$