Question

let y=(f(x))^3 and suppose that f'(1)=4 and dy/dx=10 when x=1 find f(1)​

Answer 1

Answer:

Step-by-step explanation

y=[f(x)]3

⇒y'=3f2 f'

Given:

• f'(1)=4    

• y'(1)=10    ⇒(3f2(1)f'(1)=10    

f'(1)/3f 2(1)f'(1)=4/10

1/3f2 (1)=4/10

f2(1)=10/12

f(1)=√10/12

Answer 2

Given:

$\begin{array}{l}y=[f(x)]^{3} \quad\left[=f^{3}\right] \\\Rightarrow y^{\prime}=3 f^{2} f^{\prime}\end{array}$

$\begin{array}{l}f^{\prime}(1)=4 \quad \Delta \\y^{\prime}(1)=10 \quad \Rightarrow\left(3 f^{2}(1) f^{\prime}(1)=10\right.\end{array}$

$\text { Find } f(1) \text { : }$

$\begin{array}{l}\frac{\Delta}{\square} \Rightarrow \frac{f^{\prime}(1)}{3 f^{2}(1) f^{\prime}(1)}=\frac{4}{10} \\\Rightarrow \frac{1}{3 f^{2}(1)}=\frac{4}{10}\end{array}$