Find the difference quotient
mula1" title="\frac{f(x + h) - f(x)}{h}" alt="\frac{f(x + h) - f(x)}{h}" align="absmiddle" class="latex-formula"> for the following function.
2 answers:
Answer:
Step-by-step explanation:
Step 1: Define
Difference Quotient:
f(x) = -x² - 3x + 1
f(x + h) means that x = (x + h)
f(x) is just the normal function
Step 2: Find difference quotient
- <u>Substitute:</u>
- <u>Expand and Distribute:</u>
- <u>Distribute:</u>
- <u>Combine like terms:</u>
- <u>Factor out </u><em><u>h</u></em><u>:</u>
- <u>Simplify:</u>
Hey there!
We know that formula for the difference quotient is [ ]
We need to find f(x + h), so use (x + h) instead of x.
f(x + h) → -(x + h)² because we are given [ -x² ]
-3(h + x) + 1 because we are given [ -3x + 1 ]
Put what we found into the formula and simplify.
Therefore, the difference quotient for the given function is [ -h - 2x - 3 ]
Best of Luck!
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Step-by-step explanation:
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