question 3 (2 points)\n(03.04)\ncalculate the average rate of change for the function ( f(x)=-x^{4}+4x^{3}-2x…

question 3 (2 points)\n(03.04)\ncalculate the average rate of change for the function ( f(x)=-x^{4}+4x^{3}-2x^{2}+x + 1 ), from ( x = 0 ) to ( x = 1 ).\no a 0\no b 1\no c 2\no d 7

question 3 (2 points)\n(03.04)\ncalculate the average rate of change for the function ( f(x)=-x^{4}+4x^{3}-2x^{2}+x + 1 ), from ( x = 0 ) to ( x = 1 ).\no a 0\no b 1\no c 2\no d 7

Answer

Explanation:

Step1: Recall the average rate of change formula

The average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 0), (b=1).

Step2: Calculate (f(0))

Substitute (x = 0) into (f(x)=-x^{4}+4x^{3}-2x^{2}+x + 1). (f(0)=-(0)^{4}+4(0)^{3}-2(0)^{2}+0 + 1=1).

Step3: Calculate (f(1))

Substitute (x = 1) into (f(x)=-x^{4}+4x^{3}-2x^{2}+x + 1). (f(1)=-(1)^{4}+4(1)^{3}-2(1)^{2}+1 + 1=-1 + 4-2 + 1+1=3).

Step4: Calculate the average rate of change

Using the formula (\frac{f(1)-f(0)}{1 - 0}), substitute (f(1)=3) and (f(0)=1). (\frac{3-1}{1-0}=\frac{2}{1}=2).

Answer:

C. 2