Evaluate the difference quotient for the given function.f(x)=4+3x−x2,f(3+h)−f(3)h

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Alix Ortiz · Accepted Answer

Solution:f(x)=4+3x−x2, thusf(3+h)=4+3(3+h)−(3+h)2&amp;nbsp;=4+9+3h−(9+6h+h2)=4−3h−h2&amp;nbsp;f(3+h)−f(3)h=(4−3h−h2)−4h&amp;nbsp;=h(−3−h)h=−3−h&amp;nbsp;Answer:&amp;nbsp;f(3+h)−f(3)h=−3−h

Andre BalkonE · Accepted Answer

Answer:−3−hExplanation:First, let&#039;s find f(3+h):f(3+h)=4+3(3+h)−(3+h)2Simplifying this expression:f(3+h)=4+9+3h−(9+6h+h2)f(3+h)=13+3h−9−6h−h2f(3+h)=4−3h−h2Now, let&#039;s find f(3):f(3)=4+3(3)−32Simplifying this expression:f(3)=4+9−9f(3)=4Finally, we can calculate the difference quotient:f(3+h)−f(3)h=(4−3h−h2)−4hSimplifying this expression:f(3+h)−f(3)h=−3h−h2hf(3+h)−f(3)h=h(−3−h)hf(3+h)−f(3)h=−3−hTherefore, the difference quotient for the given function is −3−h.

xleb123 · Accepted Answer

Solution:Substitute the value of x in the function with 3+h:f(3+h)=4+3(3+h)−(3+h)2Evaluate f(3) by substituting x with 3 in the function:f(3)=4+3(3)−(3)2Plug in the values into the difference quotient formula:f(3+h)−f(3)h=(4+3(3+h)−(3+h)2)−(4+3(3)−(3)2)h

fudzisako · Accepted Answer

Step 1: Substitute the values into the function.We need to find f(3+h)−f(3)h. Let&#039;s substitute these values into the function:f(3+h)=4+3(3+h)−(3+h)2 and f(3)=4+3(3)−(3)2.Step 2: Simplify the expressions.Now, we simplify the expressions inside the function:f(3+h)=4+9+3h−(9+6h+h2) and f(3)=4+9−9.Step 3: Expand and combine like terms.Expand and simplify the expressions further:f(3+h)=13+3h−9−6h−h2 and f(3)=4.Step 4: Evaluate the difference quotient.Now, let&#039;s substitute these values back into the difference quotient:f(3+h)−f(3)h=(13+3h−9−6h−h2)−4hStep 5: Simplify the expression.Simplify the expression by combining like terms:13+3h−9−6h−h2−4h=(3h−6h)+(13−9−4)−h2hStep 6: Further simplify and factor out a negative sign:−3h+0−h2h=−h2−3hhStep 7: Cancel out common factors.We can cancel out the common factor of h:−h(h+3)h=−h−31=−h−3Therefore, the difference quotient for the given function f(x)=4+3x−x2 is −h−3, which can also be written as −3−h.

Evaluate the difference quotient for the given function. Simplify your answer.

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