Finding constants given an equation, finding the simplified expression to find f', and finding f' of various numbers.

Question

Let f(x)=−1+5x2. If h≠0, then the difference quotient can be simplified as

f(x+h)−f(x)h=Ah+Bx+C,

1.

where A, B, and C are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants.

A=

B=

C=

2.

Use the simplified expression to find f′(x)=limh→0f(x+h)−f(x)h=

3.

Finally, find each of the following:

f′(1)=

f′(2)=

and f′(3)

I don't know what I'm supposed to do for part 1.

Is part 2:

5x^2+5x  ??

And I think I need part 2 to be correct in order to do part 3.

Answer 1

Garrett

For 1.

The difference quotient = ( f(x+h) - f(x)) / h = ( -1 + 5 (x+h)² - (-1 + 5x²)) / h = (10xh + 5h²) / h = 10x + 5h

So 10x +5h = Ah + Bx + C. So A=5 B = 10 C = 0

For 2. Lim h > 0 of difference quotient is obviously 10x

For 3. In (2) you have found f'(x). So you just use this here substituting the given x values

Mike

Answer 2

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