Given f(x)=4x^2+2x-9, what is f'(a)?
A. f'(a)=6a+2
B. f'(a)=6a-9
C. f'(a)=8a+2
D. f'(a)=4a+2-9
f'(x) = 8x+2
so ...
It's C?
yea its c
To find the derivative of a function f(x), we can use the power rule. The power rule states that the derivative of x^n, where n is a constant, is nx^(n-1).
For the given function f(x) = 4x^2 + 2x - 9, we will differentiate each term separately.
The derivative of the first term, 4x^2, can be found using the power rule. The exponent 2 becomes the coefficient, and x^2 becomes x^(2-1) = x^1 = x. Therefore, the derivative of 4x^2 is 8x.
The derivative of the second term, 2x, is simply 2.
The derivative of the third term, -9, is 0 since it is a constant.
Summing up the derivatives of each term, we get:
f'(x) = 8x + 2
To find f'(a), we substitute a for x in the derivative:
f'(a) = 8a + 2
Comparing the expression with the options given:
A. f'(a)=6a+2 (Not a match)
B. f'(a)=6a-9 (Not a match)
C. f'(a)=8a+2 (Matches)
D. f'(a)=4a+2-9 (Not a match)
Therefore, the correct answer is C. f'(a) = 8a + 2.