Questions: 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

Solution

Solution Steps

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

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

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

$f(x+h) = -2(1+1)^2 + 1(1+1) - 7 = -2 + 2_-2_1 - 2_1^2 + 1 + 1_1 - 7$

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

$f(x+h) - f(x) = (-2 + 2_-2_1 - 2_1^2 + 1 + 1_1 - 7) - (-2 + 1 - 7) = 2_-2_1 - 2_1^2 + 1_1$

Step 4: Simplify the difference quotient for quadratic function

$\frac{f(x+h)-f(x)}{h} = \frac{2_-2_1 - 2_1^2 + 1_1}{h} = -5$

Final Answer: The difference quotient is $-5$

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!