Questions: Given the following function, determine the difference quotient, (f(x+h)-f(x))/h. f(x)=-2x^2+x-7

Given the following function, determine the difference quotient, (f(x+h)-f(x))/h. f(x)=-2x^2+x-7
Transcript text: Question 8 of 13 , step 1 or 1 Correct Given the following function, determine the difference quotient, $\frac{f(x+h)-f(x)}{h}$. \[ f(x)=-2 x^{2}+x-7 \] Answer
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Solution

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Solution Steps

Step 1: Compute f(x+h)f(x+h) for quadratic function

Given f(x)=ax2+bx+cf(x) = ax^2 + bx + c, f(x+h)=a(x+h)2+b(x+h)+c=−2(x+1)2+1(x+1)−7f(x+h) = a(x+h)^2 + b(x+h) + c = -2(x+1)^2 + 1(x+1) - 7

Step 2: Expand and simplify f(x+h)f(x+h) for quadratic function

f(x+h)=−2(1+1)2+1(1+1)−7=−2+2−21−212+1+11−7f(x+h) = -2(1+1)^2 + 1(1+1) - 7 = -2 + 2_-2_1 - 2_1^2 + 1 + 1_1 - 7

Step 3: Find the difference f(x+h)−f(x)f(x+h) - f(x) for quadratic function

f(x+h)−f(x)=(−2+2−21−212+1+11−7)−(−2+1−7)=2−21−212+11f(x+h) - f(x) = (-2 + 2_-2_1 - 2_1^2 + 1 + 1_1 - 7) - (-2 + 1 - 7) = 2_-2_1 - 2_1^2 + 1_1

Step 4: Simplify the difference quotient for quadratic function

f(x+h)−f(x)h=2−21−212+11h=−5\frac{f(x+h)-f(x)}{h} = \frac{2_-2_1 - 2_1^2 + 1_1}{h} = -5

Final Answer: The difference quotient is −5-5

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