Find the derivative of f(x)=7x-19 at x=2.
I think that the derivative would be 7 and theb times 2 so 14. Is this correct or would it just be 7.
derivative of f(x)=7x-19 at x=2
f'(x) = 7
f'(2) = 7
f'(x)=7
for all values of x
Thank You
To find the derivative of a function, we use the process of differentiation. In this case, you want to find the derivative of f(x) = 7x - 19 at x = 2. The derivative measures the rate of change of the function at a specific point.
To find the derivative, you can use the power rule, which states that the derivative of x^n is equal to n*x^(n-1).
Applying the power rule, the derivative of f(x) = 7x - 19 is:
f'(x) = 7*1*x^(1-1) - 0
= 7*1*x^0
= 7*1*1
= 7
Therefore, the derivative of f(x) = 7x - 19 is 7.
However, to find the value of the derivative at x = 2, you need to substitute x = 2 into the derivative function. So, plugging in x = 2 into f'(x) = 7:
f'(2) = 7
Hence, the value of the derivative of f(x)=7x-19 at x = 2 is 7, not 14.