By first principle, Find the derivative of the function
iii.) f(x) = 3x^2 + 2x + 1
with respect to x at x = x subscript 0
And using the result, find the value of y at :
X_0 = 2
X_0 = 1/2
To find the derivative of the function f(x) = 3x^2 + 2x + 1, we will first calculate the derivative by differentiating each term with respect to x:
f'(x) = d/dx(3x^2) + d/dx(2x) + d/dx(1)
f'(x) = 6x + 2
Now, to find the value of the derivative at x = x0, we substitute x0 into f'(x):
f'(x0) = 6(x0) + 2
a) For x0 = 2:
f'(2) = 6(2) + 2 = 12 + 2 = 14
Therefore, the value of the derivative at x = 2 is 14.
b) For x0 = 1/2:
f'(1/2) = 6(1/2) + 2 = 3 + 2 = 5
Therefore, the value of the derivative at x = 1/2 is 5.