If f'(a)=2 and g(x)=f(x)-5, then g'(a) =
To find the value of g'(a), we need to differentiate the function g(x) with respect to x and then substitute x = a into the derivative
To find the value of g'(a), we need to differentiate the function g(x) with respect to x and then substitute x = a into the derivative.
Given that g(x) = f(x) – 5, we need to differentiate both sides of the equation with respect to x to find g'(x):
d/dx [g(x)] = d/dx [f(x) – 5]
On the left-hand side, the derivative of g(x) is g'(x), and on the right-hand side, the derivative of a constant -5 is 0 since it does not depend on x:
g'(x) = f'(x) – 0 = f'(x)
So, g'(x) = f'(x).
Now, substitute x = a into the equation to find g'(a):
g'(a) = f'(a)
Since it is given that f'(a) = 2, we can conclude that g'(a) = 2.
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