Find the derivative of the function (f(x) = x^3 - 4x^2 + 6x - 2), and then simplify the expression (|f'(2)|).

Question

Find the derivative of the function (f(x) = x^3 - 4x^2 + 6x - 2), and then simplify the expression (|f&#x27;(2)|).

Accepted Answer

Step:1 ：First, we find the derivative of the function (f(x) = x^3 - 4x^2 + 6x - 2). Using the power rule for derivatives, we have (f&#x27;(x) = 3x^2 - 8x + 6).Step:2 ：Then, we substitute (x = 2) into (f&#x27;(x)), giving us (f&#x27;(2) = 3(2)^2 - 8(2) + 6 = 12 - 16 + 6 = 2).Step:3 ：Finally, we simplify the absolute value expression (|f&#x27;(2)|). Since (f&#x27;(2) = 2) and 2 is positive, we have (|f&#x27;(2)| = |2| = 2).

Answer

Step: 1 ：First, we find the derivative of the function (f(x) = x^3 - 4x^2 + 6x - 2). Using the power rule for derivatives, we have (f&#x27;(x) = 3x^2 - 8x + 6).Step: 2 ：Then, we substitute (x = 2) into (f&#x27;(x)), giving us (f&#x27;(2) = 3(2)^2 - 8(2) + 6 = 12 - 16 + 6 = 2).Step: 3 ：Finally, we simplify the absolute value expression (|f&#x27;(2)|). Since (f&#x27;(2) = 2) and 2 is positive, we have (|f&#x27;(2)| = |2| = 2).

Find the derivative of the function $f (x) = x^{3} - 4 x^{2} + 6 x - 2$ , and then simplify the expression $| f^{'} (2) |$ .

Answer

Popular Problems

Find the derivative of the function f(x)=x3−4x2+6x−2, and then simplify the expression |f′(2)|.

Answer

Popular Problems

Find the derivative of the function $f (x) = x^{3} - 4 x^{2} + 6 x - 2$ , and then simplify the expression $| f^{'} (2) |$ .