Find the derivative of f(x) = 6x + 2 at x = 1. 1 2 3 6

2 answers:

7 0

$f(x)=6x+2,\ x_0=1\\\\f'(x_0)=\lim\limits_{h\to0}\dfrac{f(x_0+h)-f(x_0)}{h}\\\\f'(1)=\lim\limits_{h\to0}\dfrac{f(1+h)-f(1)}{h}=\lim\limits_{h\to0}\dfrac{6(1+h)+2-[6(1)+2]}{h}\\\\=\lim\limits_{h\to0}\dfrac{(6)(1)+(6)(h)-(6+2)}{h}=\lim\limits_{h\to0}\dfrac{6+6h-8}{h}\\\\=\lim\limits_{h\to0}\dfrac{6h-2}{h}=\lim\limits_{h\to0}\left(\dfrac{6h}{h}-\dfrac{2}{h}\right)=\lim\limits_{h\to0}\left(6-\dfrac{2}{h}\right)=6\\\\Answer:\ \boxed{f'(1)=6}$

marysya [2.9K]3 years ago

4 0

Ich would das that the derivative of
f(x) = 6x+2
is 6
because of derivative 6x it is 6 and the derivative of 2 is 0

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The value of a $3000 computer decreases about 30% each year. write a function for the computers value V(t)

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Answer:

Function for given situation is : $V(t)=3000(0.70)^t$

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Step-by-step explanation:

Given that the value of a $3000 computer decreases about 30% each year. Now we need to write a function for the computers value V(t). then we need to find about how much will the computer be worth in 4 years.

It clearly says that value decreases so that means function represents decay.

For decay we use formula:

$A=P(1-r)^t$