Evaluate the difference quotient
F(x)= (x+h)-f(x)
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H
A.) f(x)= 3x -1
so far i have done this
f(x+h) = 3(x+h)-1
b.) f(x)=2X^2 + 3X
i have done this f(x+h)= 2(x+h)+3(x+h)
im not sure if my answers are right.. just need some advice if they are wrong and explain what i did wrong
i just noticed i forgot to divide by h and forgot the -f(x):ooooooo but still can anyone post the answers so i know if im doing this right or wrong
is that really F(x)= (x+h)-f(x) or F(x)= f(x+h)-f(x) ? *the f(x+h)*
anyway,
A.) that's right. f(x+h) = 3(x+h)- 1
B.) you forgot to raise 2(x+h).. by 2.
also for the -f(x) in the different quotient i think i also forgot to insert 3x-1 and 2x^2+3x into my equation.... anyone
-f(x) means you just have to multiply every term by -1, like for (A)
-(3x-1) = -3x + 1
try it to letter (B). :)
then substitute the answers you get into the F(x).
To evaluate the difference quotient for the given functions, we need to substitute the expressions for f(x+h) and f(x) into the formula and simplify.
Let's start with the function f(x) = 3x - 1.
a.) To find f(x+h), we substitute (x+h) into the function:
f(x+h) = 3(x+h) - 1 = 3x + 3h - 1
Now we can substitute f(x+h) and f(x) into the difference quotient:
F(x) = (x+h) - f(x) / h = (x + h) - (3x - 1) / h
To simplify this expression, distribute the negative sign:
F(x) = (x + h) - 3x + 1 / h
= x + h - 3x + 1 / h
= -2x + h + 1 / h
So, the difference quotient for f(x) = 3x - 1 is -2x + h + 1 / h.
Now let's move on to the function f(x) = 2x^2 + 3x.
b.) To find f(x+h), we substitute (x+h) into the function:
f(x+h) = 2(x+h)^2 + 3(x+h)
= 2(x^2 + 2hx + h^2) + 3x + 3h
= 2x^2 + 4hx + 2h^2 + 3x + 3h
Now we substitute f(x+h) and f(x) into the difference quotient:
F(x) = (x+h) - f(x) / h = (x + h) - (2x^2 + 3x) / h
To simplify this expression, distribute the negative sign:
F(x) = (x + h) - 2x^2 - 3x / h
= x + h - 2x^2 - 3x / h
= -2x^2 - 2x + h / h
So, the difference quotient for f(x) = 2x^2 + 3x is -2x^2 - 2x + h / h.
Please note that it seems there was a mistake in your calculation for the second function (b), where you wrote f(x+h) = 2(x+h) + 3(x+h). The correct expression should be 2(x^2 + 2hx + h^2) + 3x + 3h.