How do you simplify f(x)=2x+3 with using the formula f(x+h)-f(x)/h?

Question

How do you simplify f(x)=2x+3 with using the formula f(x+h)-f(x)/h?

Answer 1

how do you simplify f(x)=2x+3 with using the formula f(x+h)-f(x)/h?

f(x) = 2x + 3

f(x+h) = 2(x+h) + 3

f(x+h)-f(x)/h = [2(x+h) + 3 - (2x + 3)]/h

f(x+h)-f(x)/h = [2x+2h+ 3 - 2x - 3)]/h

f(x+h)-f(x)/h = (2h)/h

f(x+h)-f(x)/h = 2

Answer 2

What do you mean? f(x) cannot be simplified further.

Answer 3

This is called differential, and you want to know the limit for (x) as (h) tends to zero (lim h→0)

You want to know [d/dx f(x)] or [f'(x)]

Yes, technically it is simplification

Please take note of the expression, you shor brackets, we do know what you mean, and asking, but expresion is important. either write

f(x) = [ f(x + h) - f(x)] / h

or

f(x) = f(x + h)/h - f(x)/h

anyway

f(x) = 2x + 3

f(x+h) = 2(x+h) + 3 = 2x + 2h + 3

d/dx f(x)

= "lim h→0" [ f(x + h) - f(x) ] / h

now substitute f(x+h) and f(x) with the above functions

= "lim h→0" [(2x + 2h + 3) - (2x + 3)] / h

= "lim h→0" [2x + 2h + 3 - 2x - 3] / h

= "lim h→0" [2x - 2x + 2h + 3 - 3] / h       {group terms}

= "lim h→0" [2h] / h           {simplified}

now you "remove" ("lim h→0"), then simplify algebraically

// = 2h / h // -- NOTE, keep this in your imagination, can't write this, because it will be an error in your differential, then cancel out (h), the answe is below

= 2          {answer}

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TIP: differentials is all about the TANGENT LINE,

or the trigonometric function TAN,

or tan(θ) = y/x = sin(θ)/cos(θ)

take note, tangent line is a stright line, f(x) = mx + c

it has a slope, m = (f(x) - c)/x   <<< whats happening here? it looks like [f(x+h) - f(x)]/h

now, d/dx g(x) = g'(x) is:

the SLOPE (m) of the straight line

the instantanuous rate of change in g(x)

Through your study in calculus, LIST ALL THE PROPERTIES of the tangent line, and study it WELL, because tan-line is extremely important, know it

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I hope this helps

love

@}'-,-'-,-

Answer 4

(f(x+h)-f(x))/h is the differential of f(x)

so

(f(x+h)-f(x))/h=f(x)'=2

Answer 5

im supporting the first answer,

im not sure the answer is correct but the process is right  

Answer 6

Your question should be to simplify f(x+h)-f(x)/h for f(x)=2x+3, otherwise it doesn't make sense.

{[2(x+h)+3] - [2x+3]} / h

= [2x + 2h + 3 - 2x - 3]/h

= 2h/h

= 2