If f(x)=sqrt(14x)
a)find f' (x)
b) find f'(4)
To find the derivative of the function f(x) = √(14x), you can use the power rule for derivatives.
a) To find f'(x), follow these steps:
Step 1: Write the function in terms of a fractional exponent: f(x) = (14x)^(1/2).
Step 2: Apply the power rule by multiplying the exponent by the coefficient and subtracting 1 from the exponent. In this case, the coefficient is 1/2.
f'(x) = (1/2) * 14 * x^(1/2 - 1)
= (1/2) * 14 * x^(-1/2)
= (7/2) * x^(-1/2)
= (7/2) * 1/√x
= 7/ (2√x)
Therefore, f'(x) = 7 / (2√x).
b) To find f'(4), substitute x = 4 into the derivative function:
f'(4) = 7 / (2√4)
= 7 / (2 * 2)
= 7/4.
Therefore, f'(4) = 7/4.