Difference Quotient fo f(x) = 3x^3 - x^2 + 7x - 1

[leeshialee]

If f(x)= 3x^3-x^2 +7x-1 find f(a-h)-f(a)
9

I have to use the difference quotient and the factoring of the cubed root is confusing me. Thanks!

Shouold I factor the x out first then proceed?

 

[mmm4444bot]

Did you proofread your post before submitting it? (Use the Preview button.)

Is the 9 that you typed part of this exercise?

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With algebraic fractions, we basically need to use grouping symbols to clearly show what is in the numerator and what is in the denominator.

I'll take a guess at your given expression.

[f(a - h) - f(a)]/9

I would not begin by factoring the expression that defines f(x). Here are the steps that I would follow.

Determine the expression f(a - h).

Determine the expression f(a).

Subtract the latter from the former.

Multiply the result by 1/9.

Simplify.

If you would like more help with this exercise, then please show whatever work you can do and explain what you're thinking, so that I might determine where to continue helping.

If I wrote anything that you do not understand, then please let me know.

 

[leeshialee]

Re: Difference Quotient Please help!

Sorry about the typo's.

This is what I have so far.

f(a+h)= 3(a+h)(a^2+2ah+h^2)-(a+h)^2+7(a-h)-1

This is the part I am confused about. Should I factor out the second (a+h)^2 so that they cancel out.

 

[mmm4444bot]

You need to multiply everything out, in order to see what the coefficients are on the a^2 term, the ah term, and the h^2 term. This is the only way to subtract f(a).

After you subtract the expression a^2 - 2ah + h2 from the expanded expression for f(a - h), multiply the result by 1/9.

I get the following result.

a h^2 - a^2 h - (1/3) h^3 - (1/9) h^2 - (7/9) h + (2/9) a h

(This exercise is a preview of what you can expect to be doing in an introductory calculus course.)