Given a function ( f(x) = 2x^2 + 3x + 1 ), find the average rate of change of ( f ) on the interval ( [1, 4] ).

Question

Accepted Answer

Step:1 ：Step 1: Substitute ( x = 1 ) into the function, we get ( f(1) = 2(1)^2 + 3*1 + 1 = 6 ).Step:2 ：Step 2: Substitute ( x = 4 ) into the function, we get ( f(4) = 2(4)^2 + 3*4 + 1 = 41 ).Step:3 ：Step 3: The average rate of change of ( f ) on the interval ( [1, 4] ) is equal to ( frac{f(4) - f(1)}{4 - 1} ).Step:4 ：Step 4: Substitute the results from Step 1 and Step 2 into the formula above, we get ( frac{41 - 6}{4 - 1} = frac{35}{3} ).

Answer

Step: 1 ：Step 1: Substitute ( x = 1 ) into the function, we get ( f(1) = 2(1)^2 + 3*1 + 1 = 6 ).Step: 2 ：Step 2: Substitute ( x = 4 ) into the function, we get ( f(4) = 2(4)^2 + 3*4 + 1 = 41 ).Step: 3 ：Step 3: The average rate of change of ( f ) on the interval ( [1, 4] ) is equal to ( frac{f(4) - f(1)}{4 - 1} ).Step: 4 ：Step 4: Substitute the results from Step 1 and Step 2 into the formula above, we get ( frac{41 - 6}{4 - 1} = frac{35}{3} ).

Given a function $f (x) = 2 x^{2} + 3 x + 1$ , find the average rate of change of $f$ on the interval $[1, 4]$ .

Answer

Popular Problems

Given a function f(x)=2x2+3x+1, find the average rate of change of f on the interval [1,4].

Answer

Popular Problems

Given a function $f (x) = 2 x^{2} + 3 x + 1$ , find the average rate of change of $f$ on the interval $[1, 4]$ .