find f''(x) if f(x)= 3(�ãx2-2x+1)
Not sure what ã means. If your f(x) is
3sqrt(x^2 - 2x + 1) then it's just 3(x-1)
'splain what the symbol means and you can get some help. Different browsers display extended symbols in different ways.
its like a sub three times the squareroot of x^2-2x+1
oh, so you mean cube root? We can write that as a power:
f(x) = 3(x^2 - 2x + 1)^1/3 = 3(x-1)^2/3
f' = 3 * 2/3 (x-1)^-1/3
= 2/(x-1)^1/3
To find the second derivative of the function f(x) = 3(x^2 - 2x + 1), we need to differentiate the function twice. Here are the steps to find f''(x):
Step 1: Find the first derivative f'(x)
To find the first derivative, you can use the power rule and the constant multiple rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1). The constant multiple rule states that the derivative of k*f(x), where k is a constant, is k times the derivative of f(x).
Differentiating f(x) with respect to x:
f'(x) = 3 * [(d/dx)(x^2) - (d/dx)(2x) + (d/dx)(1)]
Applying the power rule and constant multiple rule:
f'(x) = 3 * [2x - 2]
Simplifying:
f'(x) = 6x - 6
Step 2: Find the second derivative f''(x)
To find the second derivative, we differentiate the first derivative obtained in Step 1.
Differentiating f'(x) with respect to x:
f''(x) = d/dx(6x - 6)
Applying the power rule and constant multiple rule:
f''(x) = 6
So, the second derivative of f(x) = 3(x^2 - 2x + 1) is f''(x) = 6.