b) f(x) = 3𝑥2; 𝑑𝑓𝑑𝑥(1)= therefore the function is
Question
b) f(x) = 3𝑥2; 𝑑𝑓𝑑𝑥(1)= therefore the function is
Solution
The function f(x) = 3x^2 is a simple quadratic function. To find the derivative of this function, we use the power rule for differentiation, which states that the derivative of x^n, where n is any real number, is n*x^(n-1).
Step 1: Identify the power of x, which is 2 in this case.
Step 2: Apply the power rule. The derivative of x^2 is 2*x^(2-1) = 2x.
Step 3: Since the original function was 3x^2, we multiply the derivative of x^2 by 3. So, the derivative of 3x^2 is 3*2x = 6x.
Step 4: To find the derivative at the point x=1, we substitute x=1 into the derivative. So, df/dx at x=1 is 6*1 = 6.
Therefore, the derivative of the function f(x) = 3x^2 at the point x=1 is 6.
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