Simplify the difference quotient f ( x + h ) â f ( x ) h for the function f ( x ) = 6 x â x 2

Mathematics

1 answer:

ladessa [460]3 years ago

5 0

Answer:

final answer is 6

Step-by-step explanation:

Given $f(x)=6x-2$

To find the difference quotient use formula

$\frac{f(x+h)-f(x)}{h}$

$f(x)=6x-2$

$f(x+h)=6(x+h)-2=6x+6h-2$

Now plug it in the formula

$\frac{f(x+h)-f(x)}{h}$

$\frac{6x+6h-2-(6x-2)}{h}$

$\frac{6x+6h-2-6x+2)}{h}$

$\frac{6h}{h}$

You might be interested in

4.9t+0.3=5.6t+0.72 I need help on my work lol

Whitepunk [10]

The first step that we must take before attempting to solve the problem is to understand what the problem is asking us to do and what is given to us to help accomplish that goal. Although it does not explicitly state that we must solve for t, this is usually what the problem statement would be asking if we just receive and expression like this. What is given to us to accomplish that goal is the expression $4.9t+0.3=5.6t+0.72$ .

Now that we have completed that step, we can move onto the next part which is actually solving the problem. The next step that we should take when solving for the unknown, in this case t, is to subtract 4.9t from both sides.

Subtract 4.9t from both sides

$4.9t+0.3=5.6t+0.72$

$(4.9t-4.9t)+0.3=(5.6t-4.9t)+0.72$

$0.3=(5.6t-4.9t)+0.72$

$0.3=(0.7t)+0.72$

Now that we got all of the t's to one side, let us isolate t completely and the next step that we should take is to subtract 0.72 from both sides.

Subtract 0.72 from both sides

$0.3=0.7t+0.72$

$0.3 - 0.72=0.7t+0.72 - 0.72$

$0.3 - 0.72=0.7t$

$-0.42=0.7t$

The final step that we need to take to isolate t would be to divide both sides by 0.7 which would remove the coefficient from the unknown variable t and divide 0.7 from -0.42

Divide both sides by 0.7