For the following function, state the derivative and evaluate f'(4):
f(x) = x
Please show your work! Thank you!!
can someone please please help me with this cause i have more questions like it, but i can't figure out how to do it.
f'(x) = 1
so f'(4) = 1
I hope the others are a bit more challenging
The slope of the graph of y = x is one for any x at all, including for x = 4
To find the derivative of the function f(x) = x, you can use the power rule, which states that the derivative of a function f(x) = xn is f'(x) = nx^(n-1).
Applying the power rule to f(x) = x, we have:
f'(x) = 1x^(1-1) = 1x^0 = 1.
Therefore, the derivative of f(x) = x is f'(x) = 1.
To evaluate f'(4), simply substitute x = 4 into the derivative:
f'(4) = 1.
So, the derivative of f(x) = x is 1, and f'(4) = 1.